# How do you solve the following system: 3x + 4y = 11 , x-3y=20 ?

Feb 3, 2016

The solution for the system of equations is:
color(blue)(y = -49/13

color(blue)(x =113/13

#### Explanation:

$\textcolor{b l u e}{3 x} + 4 y = 11$ .......equation $\left(1\right)$

$x - 3 y = 20$,multiplying by $3$
$\textcolor{b l u e}{3 x} - 9 y = 60$ .......equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{3 x}} + 4 y = 11$
$- \cancel{\textcolor{b l u e}{3 x}} + 9 y = - 60$

$13 y = - 49$

color(blue)(y = -49/13

Finding $x$ from equation $2$:

$x - 3 y = 20$

$x = 20 + 3 y$

$x = 20 + 3 \times \left(- \frac{49}{13}\right)$

$x = 20 - \frac{147}{13}$

$x = \frac{260}{13} - \frac{147}{13}$

color(blue)(x =113/13