Solve the system of linear equations by the method of elimination, find (x,y). $\left\{ \begin{array} { c }
- 5 x + 2 y = - 38 \
3 x - y = 23
\end{array} \right.$
A)No solution
B) $( 8,1 )$
C) $( 8 , - 1 )$
D) $\left( \frac { 3 } { 38 } , \frac { 2 } { 23 } \right)$
E) $\left( - 5 , \frac { 2 } { 23 } \right)$

Question

Solve the system of linear equations by the method of elimination, find (x,y).  $\left\{ \begin{array} { c } 
- 5 x + 2 y = - 38 \
3 x - y = 23
\end{array} \right.$  
A)No solution
B)  $( 8,1 )$
C)  $( 8 , - 1 )$
D)  $\left( \frac { 3 } { 38 } , \frac { 2 } { 23 } \right)$
E)  $\left( - 5 , \frac { 2 } { 23 } \right)$

Quizplus · Accepted Answer

Multiply the first equation by 3 and the second equation by 5, then add the two equations to eliminate y.$$3(-5x+2y=-38) \Rightarrow -15x+6y=-114$$$$5(3x-y=23) \Rightarrow 15x-5y=115$$Add the two equations:$$0+y=1$$$$y=1$$Substitute y=1 into the first equation:$$-5x+2(1)=-38$$$$-5x+2=-38$$$$-5x=-40$$$$x=8$$Therefore, the solution to the system of equations is (x,y)=(8,1).

Solve the System of Linear Equations by the Method of Elimination