# How do you solve the following linear system:  -x + y = 3, x + y = 5 ?

Apr 16, 2018

$x = 1 \mathmr{and} y = 4$

#### Explanation:

Note that the two $x$-terms are additive inverses, so if you add the two equations, the $x$-terms will be eliminated:

$\text{ "color(blue)(-x)+y = 3" } \ldots \ldots . A$
$\text{ "color(blue)(+x)+y = 5" ".......} B$

$A + B : \text{ } 2 y = 8$
$\textcolor{w h i t e}{\times \times x . \times x} y = 4$

Substitute $y = 4$ into equation $B$ to get $x = 1$

Checking in both equations gives:

$- 1 + 4 = 3$
$+ 1 + 4 = 5$