Solve the system by the method of elimination.
$$\left\{ \begin{aligned}
\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \
x - y & = - 14
\end{aligned} \right.$$
A) $\left( - \frac { 29 } { 2 } , - \frac { 1 } { 2 } \right)$
B) $\left( - \frac { 1 } { 2 } , - \frac { 29 } { 2 } \right)$
C) $\left( - \frac { 2 } { 29 } , - \frac { 2 } { 1 } \right)$
D) $( - 29 , - 15 )$
E) no solution

Question

Quizplus · Accepted Answer

First, simplify the first equation: $x + y = -12$. Then, solve the system: $x + y = -12$ and $x - y = -14$. Adding these equations gives $2x = -26$, so $x = -13$. Substituting $x = -13$ into $x + y = -12$ gives $y = 1$. The solution is $(-13, 1)$, which matches choice A.

Solve the System by the Method of Elimination {x+75+y−25=−2x−y=−14\left\{ \begin{aligned}\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \\x - y & = - 14\end{aligned} \right.⎩⎨⎧​5x+7​+5y−2​x−y​=−2=−14​

Solve the System by the Method of Elimination $\left\{ \begin{aligned}\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \\x - y & = - 14\end{aligned} \right.$