# How do you solve 4x + 5y = 11 and y = 3x - 13?

Oct 14, 2015

The solution is
$x = 4 , y = - 1$

#### Explanation:

$4 x + 5 y = 11$...equation $1$
y =color(blue)( 3x - 13....equation $2$

Solving by substitution :

Substituting equation $2$ in $1$

$4 x + 5 y = 11$
4x + 5color(blue)(( 3x - 13) = 11

$4 x + 15 x - 65 = 11$

$19 x = 11 + 65$

$19 x = 76$

$x = \frac{76}{19}$

color(blue)(x=4

Finding $y$ by substituting $x$ in equation $2$:

$y = 3 x - 13$

$y = 3 \cdot 4 - 13$

$y = 12 - 13$

color(blue)(y=-1