# How do you solve the system of linear equations  x + 2y = 7 and 2x - 3y = -5?

Mar 1, 2016

The solution for the system of equations is:
color(blue)(x=11/7

color(blue)(y= 19/7

#### Explanation:

$x + 2 y = 7$ , multiplying this equation by $2$
$\textcolor{b l u e}{2 x} + 4 y = 14$......equation $\left(1\right)$

$\textcolor{b l u e}{2 x} - 3 y = - 5$.....equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{2 x}} + 4 y = 14$

$- \cancel{\textcolor{b l u e}{2 x}} + 3 y = 5$

$7 y = 19$

color(blue)(y= 19/7

Finding $x$ from equation $1$:
$x + 2 y = 7$

$x + 2 \times \frac{19}{7} = 7$

$x + \frac{38}{7} = 7$

$x = 7 - \frac{38}{7}$

$x = \frac{49}{7} - \frac{38}{7}$

color(blue)(x=11/7