005 Sample Final A, Question 9

Question Solve the following system of equations

${\begin{aligned}2x+3y&=&1\\-x+y&=&-3\end{aligned}}$

Step 1:
Add two times the second equation to the first equation. So we are adding $-2x+2y=-6$ to the first equation.
This leads to:
${\begin{array}{rcl}0+5y&=&-5\\-x+y&=&-3\end{array}}$

Step 2:
This gives us that $y=-1.$
Now we just need to find x. So we plug in -1 for y in the second equation.
${\begin{array}{rcl}-x-1&=&-4\\-x&=&-3\\x&=&3\end{array}}$

Final Answer:
$x=3,~y=-1$