# How do you solve x+y=6 and x-y=2?

Mar 11, 2018

$x = 4$
$y = 2$

#### Explanation:

$x + y = 6 | - y$
$x = 6 - y$

$\textcolor{red}{x} - y = 2$
$\textcolor{red}{6 - y} - y = 2$
$6 - 2 y = 2 | - 6$
-2y=-4|:(-2)
$y = 2$

$x + \textcolor{b l u e}{y} = 6$
$x + \textcolor{b l u e}{2} = 6 | - 2$
$x = 4$

Mar 11, 2018

$x = 4$

#### Explanation:

We can eliminate $y$ from the equation by adding the two together, as $y + - y = y - y = 0$
We must also add the other terms.
$2 x = 8$
$x = 4$

Mar 11, 2018

$x = 4 , y = 2$

#### Explanation:

$x + y = 6$, and $x - y = 2$
You can eliminate it or subtitute it.

A. Eliminate

$x + y = 6$
$x - y = 2$
______ -
$2 y = 4 , y = 2$
And it makes $x = 4$

B. Subtitute

$x + y = 6$
$y = 6 - x$

$x - y = x - \left(6 - x\right) = 2$

$2 x - 6 = 2$
$2 x = 8 , x = 4$
$x + y = 4 + y = 6 , y = 2$