Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l }
\frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \
8 x = - y
\end{array} \right.$
A) $\left( \frac { 1 } { 2 } , - 4 \right)$
B) $( 2,4 )$
C) $( 0,0 )$
D) $\left( \frac { 1 } { 4 } , - 2 \right)$

Question

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
\frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \
8 x = - y
\end{array} \right.$
A) $\left( \frac { 1 } { 2 } , - 4 \right)$
B) $( 2,4 )$
C) $( 0,0 )$
D) $\left( \frac { 1 } { 4 } , - 2 \right)$

Quizplus · Accepted Answer

Substitute the second equation into the first equation to get $\frac { 1 } { 2 } x + 2 (-8 x) = - \frac { 31 } { 4 } $ which simplifies to $-15x = - \frac { 31 } { 4 } $. Solving for x gives $x = \frac { 31 } { 60 } $. Substituting this value of x back into the second equation gives $8 (\frac { 31 } { 60 } ) = - y $ which simplifies to $-4 = - y $. Solving for y gives $y = 4 $. Therefore, the solution to the system of equations is $( \frac { 31 } { 60 } , 4 )$.

Solve the System of Equations by the Substitution Method {12x+2y=−3148x=−y\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \\8 x = - y\end{array} \right.{21​x+2y=−431​8x=−y​

Solve the System of Equations by the Substitution Method $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \\8 x = - y\end{array} \right.$