Solve the system of linear equations below by the method of elimination. ${9x+4y=−108−7x+2y=38\left\{ \begin{array} { l } 9 x + 4 y = - 108 \\- 7 x + 2 y = 38\end{array} \right.$

A) (1,7)
B) (-8,-9)
C) (1,0)
D) (-2,2)
E) (1,-7)

Question

Solve the system of linear equations below by the method of elimination.

{9x+4y=−108−7x+2y=38\left\{ \begin{array} { l } 9 x + 4 y = - 108 \\- 7 x + 2 y = 38\end{array} \right.

A) (1,7)
B) (-8,-9)
C) (1,0)
D) (-2,2)
E) (1,-7)

Klyzer Seijuro · Accepted Answer

Final Answer : B, Explanation :   To solve the system of equations by elimination, we aim to eliminate one variable by adding or subtracting the equations. First, we can multiply the second equation by 2 to make the coefficients of   y y y   in both equations equal:Original equations:1.   9 x + 4 y = − 108 9x + 4y = -108 9 x + 4 y = − 108  2.   − 7 x + 2 y = 38 -7x + 2y = 38 − 7 x + 2 y = 38  Multiply the second equation by 2:1.   9 x + 4 y = − 108 9x + 4y = -108 9 x + 4 y = − 108  2.   − 14 x + 4 y = 76 -14x + 4y = 76 − 14 x + 4 y = 76  Now, subtract the second equation from the first to eliminate   y y y  :  9 x − ( − 14 x ) = − 108 − 76 9x - (-14x) = -108 - 76 9 x − ( − 14 x ) = − 108 − 76 23 x = − 184 23x = -184 23 x = − 184 x = − 184 / 23 x = -184 / 23 x = − 184/23 x = − 8 x = -8 x = − 8  Substitute   x = − 8 x = -8 x = − 8   into one of the original equations to find   y y y  . Using the first equation:  9 ( − 8 ) + 4 y = − 108 9(-8) + 4y = -108 9 ( − 8 ) + 4 y = − 108 − 72 + 4 y = − 108 -72 + 4y = -108 − 72 + 4 y = − 108 4 y = − 108 + 72 4y = -108 + 72 4 y = − 108 + 72 4 y = − 36 4y = -36 4 y = − 36 y = − 9 y = -9 y = − 9  Therefore, the solution to the system of equations is   x = − 8 , y = − 9 x = -8, y = -9 x = − 8 , y = − 9  , which corresponds to choice B.

Solve the system of linear equations below by the method of elimination. ${9x+4y=−108−7x+2y=38\left\{ \begin{array} { l } 9 x + 4 y = - 108 \\- 7 x + 2 y = 38\end{array} \right.$

A) (1,7)
B) (-8,-9)
C) (1,0)
D) (-2,2)
E) (1,-7)

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Solve the system of linear equations below by the method of elimination. {9x+4y=−108−7x+2y=38\left\{ \begin{array} { l } 9 x + 4 y = - 108 \\- 7 x + 2 y = 38\end{array} \right.{9x+4y=−108−7x+2y=38​ A) (1,7) B) (-8,-9) C) (1,0) D) (-2,2) E) (1,-7)

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Solve the system of linear equations below by the method of elimination. ${9x+4y=−108−7x+2y=38\left\{ \begin{array} { l } 9 x + 4 y = - 108 \\- 7 x + 2 y = 38\end{array} \right.$

A) (1,7)
B) (-8,-9)
C) (1,0)
D) (-2,2)
E) (1,-7)