# How do you solve x + y = 1 and 3x – y = 11 using substitution?

May 10, 2016

The solution for the system of equations is:
 color(green)(x = 3
 color(green)( y = -2

#### Explanation:

$x + y = 1$
 color(blue)(x = 1 - y ........equation $\left(1\right)$

$3 x - y = 11$......equation $\left(2\right)$

Solving by substitution:

Substituting equation $1$ in $2$:

$3 x - y = 11$

$3 \cdot \textcolor{b l u e}{\left(1 - y\right)} - y = 11$

$3 - 3 y - y = 11$

$3 - 4 y = 11$

$3 - 11 = 4 y$

$- 8 = 4 y$

$y = - \frac{8}{4}$

 color(green)( y = -2

Finding $x$ from equation $1 :$

 color(blue)(x = 1 - y

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

$x = 1 + 2$

 color(green)(x = 3