# How do you solve the system x+y=2 and x-y=4?

Mar 8, 2016

The solution is $\left(3 , - 1\right)$

#### Explanation:

In this case the solution can be found by using the "elimination method". Looking at the two equations I see that you have $+ y$ in equation one and $- y$ in equation two. By adding the two equations together I will "eliminate" the $y$ variable and then I can solve for $x$.

$x + y = 2$
$x - y = 4$

Add the two equation together and get:

$2 x = 6$

x = 3 Now substitute $3$ for $x$ in either equation and solve for $y$

$x + y = 2$
$3 + y = 2$
$y = - 1$
The solution is $\left(3 , - 1\right)$
Now you can, and should, verify that your answer is correct by substituting the solution in the second equation. If it works out, you have the correct answer.
$x - y = 4$
$3 - \left(- 1\right) = 4$
$4 = 4$