# How do you solve the system of linear equations 2x + 5y = 8 and -3x + y = 5?

May 10, 2016

The solution for the system of equations is
color(blue)(x = -1 , y = 2

#### Explanation:

$2 x + \textcolor{g r e e n}{5 y} = 8$........equation $\left(1\right)$

$- 3 x + y = 5$, multiplying by $5$
$- 15 x + \textcolor{g r e e n}{5 y} = 2 5$.......equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from $1$:

$2 x + \cancel{\textcolor{g r e e n}{5 y}} = 8$
$+ 15 x - \cancel{\textcolor{g r e e n}{5 y}} = - 2 5$

$17 x = - 17$

$x = \frac{- 17}{17}$

color(blue)(x = -1

Finding $y$ from equation $2$

$- 3 x + y = 5$

$y = 5 + 3 x$

$y = 5 + 3 \cdot \left(- 1\right)$

$y = 5 - 3$

color(blue)(y =2

The solution for the system of equations is
color(blue)(x = -1 , y = 2