Solve the system by substitution, if possible. $\left\{ \begin{array} { l }
- 8 x + 7 y = - 11 \
16 x + 14 y = 106
\end{array} \right.$
A)( 4, 3)
B) (16, 14)
C) (- 4, - 3)
D) (-11, 106)
E) (- 16, - 14)

Question

Solve the system by substitution, if possible.  $\left\{ \begin{array} { l } 
- 8 x + 7 y = - 11 \
16 x + 14 y = 106
\end{array} \right.$  
A)( 4, 3)
B) (16, 14)
C) (- 4, - 3)
D) (-11, 106)
E) (- 16, - 14)

Quizplus · Accepted Answer

To solve the system by substitution, we first solve one of the equations for one variable in terms of the other. Let's solve the first equation for $x$:$-8x + 7y = -11$$-8x = -11 - 7y$$x = \frac{-11 - 7y}{-8}$Now, substitute this expression for $x$ in the second equation:$16x + 14y = 106$$16\left(\frac{-11 - 7y}{-8}\right) + 14y = 106$Simplifying, we get:$-2(-11 - 7y) + 14y = 106$$22 + 14y + 14y = 106$$28y = 84$$y = 3$Now, substitute $y = 3$ back into the expression for $x$:$x = \frac{-11 - 7(3)}{-8}$$x = \frac{-11 - 21}{-8}$$x = \frac{-32}{-8}$$x = 4$Therefore, the solution is $x = 4$, $y = 3$, which corresponds to choice (A).

Solve the System by Substitution, If Possible {−8x+7y=−1116x+14y=106\left\{ \begin{array} { l } - 8 x + 7 y = - 11 \\16 x + 14 y = 106\end{array} \right.{−8x+7y=−1116x+14y=106​

Solve the System by Substitution, If Possible $\left\{ \begin{array} { l } - 8 x + 7 y = - 11 \\16 x + 14 y = 106\end{array} \right.$