Solve the system by the addition method, if possible. If a solution exists, give the value of x. $$\left\{ \begin{array} { c }
2 ( x + y ) = y - 19 \
7 ( x + 10 ) = y + 17
\end{array} \right.$$
A) $- 5$
B) $- 11$
C) $- 2$
D) $- 8$
E) no solution

Question

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $$\left\{ \begin{array} { c } 
2 ( x + y ) = y - 19 \
7 ( x + 10 ) = y + 17
\end{array} \right.$$
A) $- 5$
B) $- 11$
C) $- 2$
D) $- 8$
E) no solution

Quizplus · Accepted Answer

To solve the system by the addition method, we need to eliminate one of the variables.

First, we can simplify the equations by distributing the coefficients:

$2x + 2y = y - 19$

$7x + 70 = y + 17$

Next, we can rearrange the terms so that the like variables are lined up:

$2x - y = -19 - 2y$

$7x - y = -53$

Now, we can add the two equations together to eliminate y:

$9x = -72$

$x = -8$

So the solution is $(x,y) = (-8,25)$.

Therefore, the answer is D.

Solve the System by the Addition Method, If Possible {2(x+y)=y−197(x+10)=y+17\left\{ \begin{array} { c } 2 ( x + y ) = y - 19 \\7 ( x + 10 ) = y + 17\end{array} \right.{2(x+y)=y−197(x+10)=y+17​

Solve the System by the Addition Method, If Possible $\left\{ \begin{array} { c } 2 ( x + y ) = y - 19 \\7 ( x + 10 ) = y + 17\end{array} \right.$