Solve the system of equations by elimination, if a solution exists.
-$$\left\{ \begin{array} { l }
x + 7 y = 5 \
- 4 x + 8 y = - 20
\end{array} \right.$$
A) $x = 6 , y = 5$
B) $x = 5 , y = 0$
C) No solution
D) $x = 6 , y = - 1$

Question

Solve the system of equations by elimination, if a solution exists.
-$$\left\{ \begin{array} { l } 
x + 7 y = 5 \
- 4 x + 8 y = - 20
\end{array} \right.$$
A) $x = 6 , y = 5$
B) $x = 5 , y = 0$
C) No solution
D) $x = 6 , y = - 1$

Quizplus · Accepted Answer

To solve the system of equations by elimination, we can multiply the first equation by 4 to make the coefficients of $x$ in both equations equal in magnitude but opposite in sign. This gives us:$$4(x + 7y) = 4(5) \Rightarrow 4x + 28y = 20$$The system of equations becomes:$$\left\{ \begin{array} { l } 4x + 28y = 20 \- 4x + 8y = - 20\end{array} \right.$$Adding these equations eliminates $x$:$$36y = 0 \Rightarrow y = 0$$Substituting $y = 0$ into the first original equation:$$x + 7(0) = 5 \Rightarrow x = 5$$Therefore, the solution is $x = 5, y = 0$.

Solve the System of Equations by Elimination, If a Solution {x+7y=5−4x+8y=−20\left\{ \begin{array} { l } x + 7 y = 5 \\- 4 x + 8 y = - 20\end{array} \right.{x+7y=5−4x+8y=−20​

Solve the System of Equations by Elimination, If a Solution $\left\{ \begin{array} { l } x + 7 y = 5 \\- 4 x + 8 y = - 20\end{array} \right.$