Explanation Given Information: Theprovided system of equations: 3 x − 2 y = − 4 2 y − 3 x = − 2 Formula used: The criteria to determine the solution of the system of equations graphically is as follows: 1. If two given lines intersect at some point, then that point of intersection of the two lines is the solution of the system of equations. 2. If the two given lines are parallel, then the system of equations have no solutions. 3. If the two equations are represented by the same line, then the system of equations have infinite number of solutions. Calculation: Consider the provided system of equation: 3 x − 2 y = − 4 2 y − 3 x = − 2 Consider the first equation 3 x − 2 y = − 4 to solve for y by subtracting 3 x from both the sides of the equation as, 3 x − 2 y − 3 x = − 4 − 3 x − 2 y = − 4 − 3 x Divide by − 2 on both the sides of the above equation, − 2 y − 2 = − 4 − 2 − 3 x − 2 y = 2 + 3 2 x Now, consider the second equation 2 y − 3 x = − 2 and solve for y by adding 3 x to both the sides of the equation as, 2 y − 3 x + 3 x = − 2 + 3 x 2 y = − 2 + 3 x Divide by 2 on both the sides of the above equation, 2 y 2 = − 2 2 + 3 2 x y = − 1 + 3 2 x Now, use the two obtained equations y = 2 + 3 2 x , y = − 1 + 3 2 x to graph the system of equations. To graph the linear equations, choose some values for variable x and determine the corresponding value of the variable y for the two linear equations. Put x = − 5 in y = 2 + 3 2 x and y = − 1 + 3 2 x to obtain the value of y as, y = 2 + 3 2 ( − 5 ) = 2 + − 15 2 = 4 − 15 2 = − 11 2 And y = − 1 + 3 2 ( − 5 ) = − 1 + − 15 2 = − 2 − 15 2 = − 17 2 Similarly more values of y are obtained corresponding to different values of x shown in the table below: x Coordinates y Coordinates y = 2 + 3 2 x ( x , y ) Coordinates x Coordinates y Coordinates y = − 1 + 3 2 x ( x , y ) Coordinates − 5 −

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Chapter 13, Problem 7RE

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To calculate: The solution of the system of equations 3x−2y=−4,2y−3x=−2 by using graph.

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Chapter 13, Problem 6RE

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Chapter 13 Solutions

DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<

Ch. 13.1 - Prob. 1SR Ch. 13.1 - Prob. 2SR Ch. 13.1 - Prob. 1DE Ch. 13.1 - Prob. 2DE Ch. 13.1 - Prob. 3DE Ch. 13.1 - Prob. 4DE Ch. 13.1 - Prob. 5DE Ch. 13.1 - Prob. 6DE Ch. 13.1 - Prob. 7DE Ch. 13.1 - Prob. 8DE

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The solution of the system of equations 3 x − 2 y = − 4 , 2 y − 3 x = − 2 by using graph.

Solution Summary: The author explains the criteria to determine the solution of the system of equations graphically.

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Chapter 13 Solutions