# How do you solve the following system of equations?: x-2y=13 , 4x+3y=8?

Dec 3, 2015

The solution for the system of equations is
color(blue)(x=5,y=-4

#### Explanation:

$x - 2 y = 13$

x=color(blue)(13+2y.....equation $1$

$4 x + 3 y = 8$.....equation $2$

Solving by substitution :

Substituting equation $1$ in equation $2$ to find $y$

$4 x + 3 y = 8$

$4 \cdot \left(\textcolor{b l u e}{13 + 2 y}\right) + 3 y = 8$

$4 \cdot \left(\textcolor{b l u e}{13}\right) + 4 \cdot \textcolor{b l u e}{\left(2 y\right)} + 3 y = 8$

$52 + 8 y + 3 y = 8$

$52 + 11 y = 8$

$11 y = 8 - 52$

$11 y = - 44$

$y = \frac{- 44}{11}$

color(blue)(y=-4

Now, we substitute this value of $y$ in equation $1$ to find $x$
$x = 13 + 2 y$

x=13+2*color(blue)((-4)

$x = 13 - 8$

color(blue)(x=5