# How do you solve x + y = 14 and -x + y = 16?

Aug 2, 2015

The solution for the system of equations is
color(blue)(x=-1,y=15

#### Explanation:

$\textcolor{b l u e}{x} + y = 14$.......equation $\left(1\right)$
 color(blue)(−x)+y=16...equation $\left(2\right)$

Upon adding the equations color(blue)(x gets eliminated
$\cancel{\textcolor{b l u e}{x}} + y = 14$
 cancelcolor(blue)(−x)+y=16

$2 y = 30$
color(blue)(y=15

Substituting the value of $y$ in equation $\left(1\right)$ to find $x$
$x + y = 14$

$x = 14 - 15$
color(blue)(x=-1