Solve Systems of Equations with the Substitution Method

Solve this system of equations with the substitution method:

1.

Write down the equations:

$$\begin{array}{lll}\hfill \mathrm{\text{(}}\text{1}\text{)}y+2x=1& & \hfill \\ \hfill \mathrm{\text{(}}\text{2}\text{)}y-x=-2& & \hfill \end{array}$$

$$\mathrm{\text{(}}\text{1}\text{)}y+2x=1\mathrm{\text{(}}\text{2}\text{)}y-x=-2$$

2.

Choose the equation you think looks easier and solve for one of the variables: $$\begin{array}{llll}\hfill \mathrm{\text{(}}\text{1}\text{)}y+2x& =1& \hfill & \\ \hfill y& =1-2x& \hfill & \end{array}$$

3.

Insert the expression you just found into the equation you haven’t used yet: $$\begin{array}{llll}\hfill y-x& =-2& \hfill & \\ \hfill (1-2x)-x& =-2& \hfill & \\ \hfill 1-2x-x& =-2& \hfill & \\ \hfill -3x& =-2-1& \hfill & \\ \hfill \frac{-3x}{-3}& =\frac{-3}{-3}& \hfill & \\ \hfill x& =1& \hfill & \end{array}$$

4.

Put this value back into the first expression you found: $$\begin{array}{llll}\hfill y& =1-2x& \hfill & \\ \hfill y& =1-2\cdot (1)& \hfill & \\ \hfill y& =1-2& \hfill & \\ \hfill y& =-1& \hfill & \end{array}$$

5.

Write the answer in coordinate form:

$$(x,y)=(1,-1)$$