which equation is equivalent to the given equation

which equation is equivalent to the given equation

An equivalent equation is A ( x x 0)+ B ( y y 0)+ C ( z z 0) = 0, where ( x 0;y 0;z 0) is a given point in the plane. SOLUTION: Write two equations in standard form that are ... a: 9/4 - 9/4 b: y = (x - 3/2)^2 - 1/4. u00+3u0+5u=0 Use v to represent the "velocity function", i.e. Write the given third order linear equation as an ... Send. If two members of an equation are added or subtracted by the same amount, the equation is equivalent to that given. one variable when they are combined? When given an equation of the form where is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation and solve for the unknown. Step 2: Click the blue arrow to submit and see the result! "combining like terms" + lesson plan. Let's see a quick example. For example, the next two equations are equivalent, therefore, their solution yields the same value for. Multiply the second equation by −2 to get −8x − 6y = −30. Multiply the second equation by 5 and add. Which equation is equivalent to the given equation ... When we are given a set of parametric equations and need to find an equivalent Cartesian equation, we are essentially "eliminating the parameter." However, there are various methods we can use to rewrite a set of parametric equations as a Cartesian equation. Equation Solver. The system of di erential equations is therefore given by Eqs. Step 1: The given linear equation is x - 2y = 2. Which equation is equivalent to the given equation - 17357101 ashleycontreras26 ashleycontreras26 08/31/2020 Mathematics High School answered Which equation is equivalent to the given equation 1 See answer Advertisement Advertisement ashleycontreras26 is waiting for your help. that is, if the equation is satisfied when the substitutions are made. Two systems of linear equations are equivalent if and only if they have the same set of solutions. An equivalent equation (that is an equation with exactly the same solutions) is + =, with A = a, B = b, and C = -c. These equivalent variants are sometimes given generic names, such as general form or standard form. Select the correct answer. Two equations are called equivalent when the multitudes of their roots match, the roots of the first equation are also roots of the second and vice versa. In the general equation of a line y = mx + b , the m represents your slope value. Solving equations by iteration. Transcribed image text: Write a system of equations that is equivalent to the given vector equation. • 4x2 3xy 2y2 +xy +6=0isaquadraticequation,asare x 2y =0andx +y2 =0andx2 1=0. 1. Add your answer and earn points. Given a second order differential equation, write an equivalent system of first order equations with transformations. The general equation of parabola is as follows: y = a ( x − h) 2 + k o r x = a ( y − k) 2 + h, w h e r e ( h, k) d e n o t e s t h e v e r t e x. part b: what equation is equivalent to the given equation after completing the square? If we were given the system of equations: y=-4x+9. Convert the following polar equations to their rectangular forms. Example: Say point (1,2) is the center of the circle and radius is equal to 4 cm. Answer by checkley77 (12844) ( Show Source ): You can put this solution on YOUR website! An equation has an equal sign, a right side expression and a left side expression. A special case of a first-degree equation in two variables is given by. Step 1: Enter the point and slope that you want to find the equation for into the editor. The equation point slope calculator will find an equation in either slope intercept form or point slope form when given a point and a slope. 1. Notice that if we are given the equation of a plane in this form we can quickly get a normal vector for the plane. equations that have the same solution sets; in the case of multiple roots, the multiplicities of the respective roots must be equal. The given system of equations is. This actually is going to be-- It changes it the way it looks, but it actually represents the same line. Value of the unknown quantity for which from given equation we get true numerical equality is called root of that equation. Now, let's subtract 4 (four) from both sides of our equation and check if the resulting equation still is equivalent to our original x+ 4 = 9. x + 4 = 9 is our given equation. Approximately when will the object be 3 inches above the rest position? . Multiply the second equation by 2 and add. 8y-4x=40. If the differential equation is not exact as written, then there exists a function μ( x,y) such that the equivalent equation obtained by multiplying both sides of (*) by μ, . Negative eight times 2y is -16y. x+4y=3. First, write the corresponding matrix form of the given equation Ax= b A x = b where A is the square matrix. Type in any equation to get the solution, steps and graph This website uses cookies to ensure you get the best experience. Solve multivariate systems of congruences: Step 2: Convert the equation in the form of y = mx + b. this will give: y = x/2 - 1. Developing an effective predator-prey system of differential equations is not the subject of this chapter. 4x1 + 6x2 + 5x3 = 0 2X1 + 4x2 + x3 = 0 OB. (2) y = mx + c. With b and c being any constants. These possess more complicated solution sets involving one . First, by replacing the by in the first given quadratic equation with real roots and then solving for in terms of and , one gets the condition for the roots of to be real. Answer. A special case of a first-degree equation in two variables is given by. matrix-vector equation. Use v and u for the two functions, rather than u(t) and v(t). Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself. Applying either of these rules produces a new equation equivalent to the old one and thus preserves the solution. Parametric Equations. find an equivalent expression with the given denominator. Aside: Origin of the First Order Differential Equation. Examples of equations 3x + 3 = 2x + 4 : the left side of the equation is the expression 3x + 3 and the right side is 2x + 4. In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other. If you feel this article useful, like and share it with your friends. Weegy:.) Now, for a given equation (2), we present a method for constructing other first-order differential equations which are equivalent to (2), that is, to find out the solution of (6) with Two equations are said to be equivalent when they have the same solution set. Often this will be written as, \[ax + by + cz = d\] where \(d = a{x_0} + b{y_0} + c{z_0}\). u0000 u = 0 We want a system in the four unknown functions u 1, u 2, u . Which equation is equivalent to the given equation? Examples. Given a linear equation , a sequence of numbers is called a solution to the equation if. By adding these equations . Solution Multiplying each member by 6 yields f (x) = y = 25 - 5x. Get my full lesson library ad-free when you become a member. In other words, two systems are equivalent if and only if every solution of one of them is also a solution of the other. Divide both sides by 2. Solution: Let us plot the graph for the equation using the following steps. Weegy:.) Question 173745: Write two equations in standard form that are equivalent to the given equation. part a: what numeric expression should be added in order to complete the square for the given expression? The equation of parabola in standard form are as below: y 2 = 4 a x. I n t h i s p a r a b o l a f o r m, t h e f o c u s o f t h e p a r a b o l a l i e s o n t h e p o s i t i v e s i d e o f t . It's equivalent to y x =0, and y x2 is a . Given the following system of equations: 2x + 6y = 12 4x + 3y = 15 Which action creates an equivalent system that will eliminate. Convert the third order linear equation below into a system of 3 first order equation using (a) the usual substitutions, and (b) substitutions in the reverse order: x 1 = y″, x 2 = y′, x 3 = y. Deduce the fact that there are multiple ways to rewrite each n-th order linear equation into a linear system of n equations. O A. Introducing on both sides: 2. Equivalent Equations Definition Equivalent equations are ones that result in the same value. • y = x 2is a quadratic equation. Write the given second order equation as its equivalent system of first order equations. Free equations calculator - solve linear, quadratic, polynomial, radical, exponential and logarithmic equations with all the steps. The motion of a weight that hangs from a spring is represented by the equation h = 8sin ( 2pi/3 t). So she just multiplied both sides by the same value which actually doesn't change the equation. See and . Asking whether or not a vector equation has a solution is the same as asking if a given vector is a linear combination of some other given vectors. x^2 - 6x =8 - Let's ques! This is called the scalar equation of plane. Answer (1 of 2): Suppose we're given a second-order linear ordinary differential equation of the form y''+ P(x)y' + Q(x)y = f(x) where P(x) and Q(x) are analytic at x=0 and on some interval of interest, I The transformation we would use is u_1 = y u_2 = y' thus u_1' = y' and u_2' = y'' so t. u''+6u'+5u=0 Use v to represent the "velocity function", i.e. The following rules are valid: 1. This is how I look at the solution of the problem. x = 5 (just simplify both sides of our equation. System of equations with standard form. Thus, of the three equations = 2, 3x - 7 = 5, and (x - 4) 2 = 0, the first and second are equivalent but the first and third are not, since the multiplicity of the root x = 4, is equal to 1 for the first equation and 2 for the third equation. This second form is often how we are given equations of planes. When given an equation of the form where is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation and solve for the unknown. (The latter confuses webwork. The number 5 is actually the only solution . Solve: tan (x) - cos^2 (x) = sin^2 (x) [A] pi/4 + kpi. Transcribed Image Text. Video Transcript. Solve a congruence involving variables in the modulus: solve 22 = 10 mod n. Solve systems with each equation under a different modulus: x = 1 mod 2, x=3 mod 6, x=3 mod 7. When we take x = 2, we get y = - 4, therefore ( 2, - 4) is the solution of the equation. 0 Write two differential equations as an equivalent system of first order equations. Step 3: Find the x and y-intercept respectively by putting y = 0 in the equation. Negative eight times X is -8X. We can add or subtract the same number on both sides of an equation. r=Scot 0 csc e A) y 5x B) y = 5x2 Cy D) y2 = 5x. μ r 2 ϕ ˙ = L z = c o n s t. μ r ¨ = L z 2 μ r 3 − d U d r. Two examples are given below, one for a mechanical system and one for an electrical system. v=u'(t). If two members of an equation are multiplied or divided by the same number (nonzero), the equation is equivalent to that given. Ans. 2x + y = 3 2.) 4 0. 2x + 3y = 2 - 2x : equation in two variables x and y. 8. mcdougal littell integrated mathematics answers. So this right here is going to be Well, okay, so this, in terms of actors is just x two plus five, x three and then for this one is for ex woman plus six x two minus sechs three minus x +13 x two minus takes three is equal to zero vectors. Functions like sin(t) are ok.) u' = v' = Now write the system using matrices: u . Solving system a 11 x + a 12 y + a 13 z = b 1 a 21 x + a 22 y + a 23 z = b 2 a 31 x + a 32 y + a 33 z = b 3 (8) is the geometric equivalent of nding all possible ( x;y;z )-intersections of the planes represented by system (8 . Use v and u for the two functions, rather than u(t) and v(t). y = kx (k is a constant) Such a relationship is called a direct variation. fullscreen Expand. Solve the given equation, then create an equivalent equation to the given equation 9x + 3 = 15x -6. close. (r, \phi) (r,ϕ) to describe this system. answers dividing decimals by whole integers. Example 2. Because division is defined in terms of multiplication, the multiplication property of equality also allows us to divide both sides by the same nonzero number. Equations in Mathematics . by Marco Taboga, PhD. v=u0(t). Dividing the both sides by : 4 6 X1 + X3 31-10) -2 4 Choose the correct answer below. To find the vector equation that is equivalent to the given equation. Equivalent systems of equations. Graph the first equation by finding two data points. Answer (1 of 3): By completing the square, which of the following equation is equivalent to the equation of the parabola given by 4x^2 + 6x =4? 7.7 DIRECT VARIATION . If x = 0, then f (0) = 15 - 5 (0) = 15. https://www.youtube.com/channel/UCNuchLZjOVafLoIRVU0O14Q/join Plus get all my audiobooks, access. Equivalent equations are systems of equations that have the same solutions. Transcribed image text: Write the given second order equation as its equivalent system of first order equations. Example (7.1.4) Transform the given equation into a system of rst order equations. A normal vector is, by multiplying each member by 6. What does it mean when an equation is equivalent? x - 2y = -1 If equation 1 is multiplied by 2 and then the equations are added, the result is C.5x = 5 5. Example: 2 x + y = 0. 7.7 DIRECT VARIATION . Comparing this equation with the form y = mx + b, we note that the slope m (the coefficient of x) equals 2/3, and the y-intercept equals -2. use the expression x^2 + 10x − 13 to answer the following questions. 26. Step 1: Enter the Equation you want to solve into the editor. Linear Equation Problems. Example 1 Write an equivalent equation to. We are always looking for ways to improve the quality of . 6 months ago. Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to an equation of the form p(x,y)=0 where p(x,y)isaquadraticpolynomial. For example, dividing both sides by 2 is equivalent to multiplying both sides by Equations that have the same solution set are called equivalent equations. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. given are the two following linear equations: f (x) = y = 15 - 5x. Okay, so we're asked to take this system of equations and write as a vector equation. First week only $4.99! Systems of linear equations involving more than two variables work similarly, having either one solution, no solutions or infinite solutions (the latter in the case that all component equations are equivalent). The equation calculator allows you to take a simple or complex equation and solve by best method possible. factorise quadratic equation calculator. To Generate Equivalent Equations. Check if values are equivalent under a given modulus: 17 = 7 mod 10. 4x4 + 6x2 + 5x3 = 0 2X1 + 4x2 = 0 OC. u" - 8u' + 4.5u = 3 sin(3t), u(1) = 1.5, u'(1) = 3 Use v to represent the "velocity function", i.e. A rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane. 1 What is the equation of a line that has a. NeTakaya. When we take x = 0, we get y = 0, therefore ( 0, 0) is the solution of the equation. Different quantities can be placed on each side: if the weights on the two sides are equal, the scale balances, and in analogy, the equality that represents the balance is also balanced (if not, then the lack of balance corresponds to an inequality represented by . \displaystyle 4x^2 + 6x = 4 \implies x^2 + \frac{3}{2}x + = 1 \implies x^2 + \frac{3}{2}x + \frac{9}{16}= 1 + \frac{9}{16} \implies \displaystyle (x +. Definition An equation is a statement that expresses the equality of two mathematical expressions. For example the vector equation above is asking if the vector (8,16,3) is a linear combination of the vectors (1,2,6) and (− 1,2, − 1). Multiply the second equation by 2 and add. Second, by solving the quadratic equation for in terms of and getting rid of the square root with inside, one gets if . 2y-x=10. For example y = 4 x + 3 is a rectangular equation. v=u'(t). Which equation is equivalent to the given equation? x - 2y = -1 If equation 1 is multiplied by 2 and then the equations are added, the result is C.5x = 5 A curve in the plane is said to be parameterized if the set of coordinates on the curve, ( x, y) , are . 6x+24y=18. Write The Given Second Order Equation As Its Equivalent System Of First Order Equations. The new system of equation is. equation, in mathematics, a statement, usually written in symbols, that states the equality of two quantities or algebraic expressions, e.g., x+3=5.The quantity x+3, to the left of the equals sign (=), is called the left-hand, or first, member of the equation, that to the right (5) the right-hand, or second, member.A numerical equation is one containing only numbers, e.g., 2+3=5. See and . Hope that we can help you do this homework as exactly as possible. For the given polar equation, write an equivalent rectangular equation. x + 4 − 4 = 9 − 4 (we subtract 4 (four) from both sides of our equation. (1 pt) Write the given second order equation as its equivalent system of first order equations. Multiply the first equation by 2 to get 4x + 12y = 24. So, to find an equation of a line that is parallel to another, you have to make sure both equations have the same slope. This is the standard form of the equation. To solve the equation c (c ≠ 0) are equivalent equations. y+4x=9. An equation is analogous to a weighing scale, balance, or seesaw.. Each side of the equation corresponds to one side of the balance. Which equation is equivalent to the given equation? Equations of nonconstant coefficients with missing y-term If the y-term (that is, the dependent variable term) is missing in a second order linear equation, then the equation can be readily converted into a first order linear equation and solved using the integrating factor method. So this is definitely still an equivalent system. Then, we can solve using the elimination method by multiplying the second equation by 4. y+4x=9. Thus, if we know the coordinates of the center of the circle and its radius as well, we can easily find its equation. 6x+24y=18. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set. The differential equation with input f(t) and output y(t) can represent many different systems. The equation of a circle with (h, k) center and r radius is given by: (x-h) 2 + (y-k) 2 = r 2. Question. Multiply the second equation by -2 and add. It models the weight's height (in inches) above or below the rest position as a function of time (in seconds). Furthermore, conservation of angular momentum gives the constant of the motion. To use this online calculator for Diode Equation, enter Saturation current (I s), Voltage across diode (V d), Emission coefficient or ideality factor (n) & Volts-Equivalent of Temperature (V t) and hit the calculate button. Example: t y″ + 4 y′ = t 2 The standard form is y t t 5pi/4. Multiply the second equation by −4 to get −16x − 12y . Such a function μ is known as an integrating factor of the original equation and is guaranteed to exist if the given differential equation has a solution. x^2 - 6x =8. Multiply the second equation by 5 and add. Multiply the second equation by -2 and add. Select the correct . The calculator also has the ability to provide step by step solutions. Take a look at examples of equivalent equations, how to solve them for one or more variables, and how you might use this skill outside a classroom. You should then be able to write (x1',x2',x3') as a column vector equals A(x1,x2,x3) where A is your coefficient matrix and (x1,x2,x3) is a column vector. And you have known the answer to this Math question. Therefore, we need to divide the second equation by 2, to create this new equivalent system of equations. Algebra. Here is how the Diode Equation calculation can be explained with given input values -> 7.68949 = 0.01*(2.71^(100/(0.15*100 . Make sure that the resulting rectangular equation is in its standard form. +000 Right. Start your trial now! Effective Potential and the Equation of Orbit. However, systems can arise from \(n^{\text{th}}\) order linear differential equations as well. By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis. The answer is either A or B. You might be interested in. Point Slope Calculator. 2x + y = 3 2.) first order equation. After solving this. Comparing this equation with the form y = mx + b, we note that the slope m (the coefficient of x) equals 2/3, and the y-intercept equals -2. y = kx (k is a constant) Such a relationship is called a direct variation. We can multiply or divide both sides of an equation by the same number (except zero). Start with the equations x1' = x2 and x2' = x3, then rearrange the first equation to get an expression for x3' in terms of x1, x2, and x2'. Use v and u for the two functions, rather than u(t) and v(t). (3){(4): u0 1 = u 2 u0 2= 1 2 u 2u 1 Solving this system is equivalent to solving the original second order di erential equation. y-9=\frac{1}{2}x-4 …we can rewrite the equations in standard form. A sequence of numbers is called a solution to a system of equations if it is a solution to every equation in the system.. A system may have no solution at all, or it may have a unique solution, or it may have an infinite family of . As well combining like terms & quot ; combining like terms & quot ;,.... The plane with inside, one gets if next two equations are said to be -- it changes it way! To find the equation of a line that has a. NeTakaya order equations • 4x2 3xy 2y2 +xy +6=0isaquadraticequation asare. 6X =8 - Let & # x27 ; re asked to take this system of equations Write. Everyday life rectangular forms second order equation as an equivalent system of equations Solver: Wolfram|Alpha < /a answers! And a left side expression and a left side expression > Solving equations by iteration < >... And graph this website uses cookies to ensure you get the best.. You to take a simple or complex equation and solve by best method possible,! Calculator also has the ability to provide step by step solutions a right side expression and a side. Examples are given the equation for into the editor 0 ) = sin^2 ( x ) a. ( 1 pt ) Write the given linear equation as an... < /a > Algebra /a Negative. Be -- it changes it the way it looks, but it actually represents the same value for x,! The Problem X1 + X3 31-10 ) -2 4 Choose the correct equation get! To 4 cm to submit and see the result second equation which equation is equivalent to the given equation the same number on both of! Pi/4 + kpi take this system looking for ways to improve the quality of, by Solving quadratic. Their solution yields the same value for rectangular forms 4x2 + X3 = 2X1. { 1 } { 2 } x-4 …we can rewrite the equations in form. From both sides of an equation has an equal sign, a right expression. Href= '' https: //quickmath.com/webMathematica3/quickmath/graphs/equations/basic.jsp '' > differential equations - systems of equations and as! ; combining like terms & quot ; combining like terms & quot ; velocity function quot. Of and getting rid of the square for the two functions, rather than u ( t ) the... + b, the next two equations are said to be equivalent when they have the same on! The equation =8 - Let & # x27 ; s ques therefore, we can solve the... Form is often how we are given below, one for a system. From both sides by the same value which actually doesn & # 92 ; phi ) (,. ( 7.1.4 ) Transform the given equation Ax= b a x = (... Solver < /a > 5pi/4 +6=0isaquadraticequation, asare x 2y =0andx +y2 =0andx2 1=0 ) -2 4 Choose correct! 5 ( 0 ) = 15 expresses the equality of two mathematical expressions the... Of a first-degree equation in two variables x and y-intercept respectively by putting y = ( x -! A vector equation a line y = mx + b, the m represents your slope value this... Change the equation of a plane in this which equation is equivalent to the given equation we can help do. A system in the general equation of a weight that hangs from a spring represented... Is -8X numeric expression should be added in order to complete the square root with inside, one if... ( 2pi/3 t ) and v ( t ) 4 ( four ) from both sides of our equation describe. That the resulting rectangular equation mathematical expressions we need to divide the second by. First, Write the corresponding matrix form of the square matrix represent many different systems side expression describe system... And radius is equal to 4 cm x + 4 − 4 ( four ) from both of! 9 − 4 = 9 − 4 = 9 − 4 = −. B. this will give: y = mx + b Generate equivalent equations (! X - 2y = 2 respectively by putting y = 5x2 Cy D ) y2 = 5x solve: (. ): you can put this solution on your website for ways improve. Is called a direct variation electrical system PDF < /span > 1 called root of that equation represent many systems! Below, one gets if ; + lesson plan equations Solver: Wolfram|Alpha < /a > eight! By checkley77 ( 12844 ) ( r, & # x27 ; t change the equation is in its form! - 1 a plane in this form we can add or subtract the same which. Notice that if we are given below, one gets if to provide by... A valuable skill, not only in Algebra < /a > equivalent systems of equations Solver: Wolfram|Alpha < >... Href= '' https: //www.youtube.com/channel/UCNuchLZjOVafLoIRVU0O14Q/join Plus get all my audiobooks, access 0 OB except zero ) except... Equations as an... < /a > matrix-vector equation sure that the resulting rectangular equation this new equivalent system first. Solve using the elimination method by multiplying the second equation by 4. y+4x=9 form we can add or the. Multiply the second equation by the same number ( except zero ) paralell. Y ( t ) can represent many different systems, Write the given we! Plus get all my audiobooks, access data points polar equations to their rectangular.... Step 2: Click the blue arrow to submit and see the result added or subtracted by same. When they have the same solution set homework as exactly as possible //www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.173745.html '' > Write the given we... A direct variation ( Show Source ): you can put this solution on your website given! The given equation Ax= b a x = b where a is the square matrix ; re to... S ques is a of first order equations get 4x + 12y = 24 u0000 u = 0 the. Complete the square matrix unknown quantity for which from given equation we get numerical...: y=-4x+9 u00+3u0+5u=0 use v to represent the & quot ;, i.e for ways to improve the quality.... This system of differential equations - systems of congruences: < a href= https. 8Sin ( 2pi/3 t ) as an... < /a > answers dividing decimals by whole.... Is called root of that equation the best experience can represent many different systems simple complex! An effective predator-prey system of rst order equations Solving equations by iteration < /a > Ans said! Provide step by step solutions k is a valuable skill, not only in Ans ) is the of... Share it with your friends: < a href= '' https: //quizlet.com/503090929/solving-trigonometric-equations-assignment-flash-cards/ '' > differential <... From given equation into a system of first order equations re asked to take a or. The elimination method by multiplying the second equation by −4 to get the best experience 9/4 9/4... 2Y =0andx +y2 =0andx2 1=0 href= '' https: //quickmath.com/webMathematica3/quickmath/graphs/equations/basic.jsp '' > Write the corresponding form... =0Andx +y2 =0andx2 1=0 that has a. NeTakaya, like and share it with your.! =0Andx +y2 =0andx2 1=0 3: find the equation < a href= '' https //www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.173745.html! Square matrix a href= '' https: //math.stackexchange.com/questions/3436304/write-the-given-third-order-linear-equation-as-an-equivalent-system-of-first-ord '' > Solving equations by iteration: //quizlet.com/503090929/solving-trigonometric-equations-assignment-flash-cards/ '' >:! Everyday life equation has an equal sign, a right side expression of these rules a... = y = kx ( k is a rectangular equation ) from both sides of equation., Examples... < /a > to Generate equivalent equations is not the subject this! The general equation of a first-degree which equation is equivalent to the given equation in two variables is given by the matrix.

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