# How do you solve the following system: 7y - 2x = 10, -3y + x = -3 ?

Dec 31, 2015

The solution for the system of equations is

color(blue)(x=9 , y=4

#### Explanation:

$7 y - \textcolor{b l u e}{2 x} = 10$...........equation $\left(1\right)$

$- 3 y + x = - 3$, multiplying by $2$:
$- 6 y + \textcolor{b l u e}{2 x} = - 6$......equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$:

$7 y - \cancel{\textcolor{b l u e}{2 x}} = 10$
$- 6 y + \cancel{\textcolor{b l u e}{2 x}} = - 6$

color(blue)(y=4

Finding $x$ from equation $2$

$- 3 y + x = - 3$

$x = - 3 + 3 y$

$x = - 3 + 3 \times 4$

$x = - 3 + 12$

color(blue)(x =9