# How do you solve the system x+y=1 and 2x-y=2?

Feb 28, 2016

$x = 1$
$y = 0$

#### Explanation:

$x + y = 1$--------------------- (1)
$2 x - y = 2$ ------------------(2)

Solving the 1st equation for $y$, we get

$y = 1 - x$

Substitute $y = 1 - x$ in equation (2)

$2 x - \left(1 - x\right) = 2$

Simplify and solve for $x$

$2 x - 1 + x = 2$
$3 x = 2 + 1$
$x = \frac{3}{3} = 1$
$x = 1$

Substitute the value $x = 1$in equation (1) and solve for $y$

$1 + y = 1$
$y = 1 - 1$
$y = 0$