# How do you solve 7x - y = 26 and x + y = 6 using substitution?

May 11, 2016

The solution for the system of equations is :
color(green)(x= 4

color(green)(y=2

#### Explanation:

$7 x - y = 26$.........equation $\left(1\right)$

$x + y = 6$,
color(blue)(y = 6 - x..............equation $\left(2\right)$

Solving by substitution :

Substituting equation $2$ in equation $1$:

$7 x - y = 26$

$7 x - \textcolor{b l u e}{\left(6 - x\right)} = 26$

$7 x - 6 + x = 26$

$7 x + x = 26 + 6$

$8 x = 32$

$x = \frac{32}{8}$

color(green)(x= 4

Finding $y$ from equation $2$
color(blue)(y = 6 - x

$y = 6 - 4$

color(green)(y=2

The solution for the system of equations is :
color(green)(x= 4

color(green)(y=2