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 to get $x + y = -8$. Then, add this to the second equation $x - y = -14$ to eliminate $y$, resulting in $2x = -22$, giving $x = -11$. Substitute $x = -11$ back into $x + y = -8$ to find $y = 3$. However, this does not match any given options, indicating a mistake in the options. Re-evaluating, the correct solution should be $(-11, 3)$, but since this is not an option, the closest match is option A, which is incorrect. The correct solution is not listed.

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 $\left\{ \begin{aligned}\frac { x + 7 } { 5 } + \frac { y - 2 } { 5 } & = - 2 \\x - y & = - 14\end{aligned} \right.$