# How do you solve the system by graphing 2x+y=10 and 3x+4y=0?

Dec 27, 2015

The solution for the system of equations is

color(blue)(x=8,y=-6

#### Explanation:

$2 x + y = 10$, multiplying by $4$
$8 x + \textcolor{b l u e}{4 y} = 40$....equation $\left(1\right)$

$3 x + \textcolor{b l u e}{4 y} = 0$.......equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from $1$:

$8 x + \cancel{\textcolor{b l u e}{4 y}} = 40$

$- 3 x - \cancel{\textcolor{b l u e}{4 y}} = - 0$

$5 x = 40$

color(blue)(x=8

Finding $y$ by substituting $x$ in equation $1$

$2 x + y = 10$

$y = 10 - 2 x$

y=10 -2 xx color(blue)(8

$y = 10 - 16$

color(blue)(y=-6