Solve Systems of Equations with the Elimination Method

Solve the system of equations.

1.

We decide to get rid of $y$.

2.

Because you have $2y$ in (2) and $y$ in (1), you have to multiply (1) by $-2$ to get rid of the $y$ value when you add the two equations together. In this case, you don’t need to multiply (2) by any factors. $$\begin{array}{llll}\hfill y+2x& =1|\cdot (-2)& \hfill & \text{(}\text{1}\text{)}\\ \hfill 2y-4x& =2& \hfill & \text{(}\text{2}\text{)}\end{array}$$

3.

Write the two equations again after making the changes. $$\begin{array}{llll}\hfill -2y-4x& =-2& \hfill & \\ \hfill 2y-x& =2& \hfill & \end{array}$$

4.

Now, add the two equations together to get rid of $y$, and solve for $x$: $$\begin{array}{llll}\hfill -2y+2y-4x-x& =-2+2& \hfill & \\ \hfill 0y-5x& =0& \hfill & \\ \hfill x& =0& \hfill & \end{array}$$

5.

Insert this answer into one of the equations. You can choose whichever one you like. I chose equation (1): $$\begin{array}{llll}\hfill y+2x& =1& \hfill & \\ \hfill y+2\cdot (0)& =1& \hfill & \\ \hfill y+0& =1& \hfill & \\ \hfill y& =1& \hfill & \end{array}$$

6.

Write the answer on coordinate form:

$$(x,y)=(0,1)$$