# 005 Sample Final A, Question 9

Question Solve the following system of equations

{\displaystyle {\begin{aligned}2x+3y&=&1\\-x+y&=&-3\end{aligned}}}
Foundations:
1) What are the two methods for solving a system of equations?
2) How do we use the substitution method?
3) How do we use the elimination method?
1) The two methods are the substitution and elimination methods.
2) Solve for x or y in one of the equations and substitute that value into the other equation.
3) Multiply one equation by some number on both sides to make one of the variables, x or y, have the same coefficient and add the equations together.

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