# How do you solve the following system:  3x – y = 28 , 2x+5y=-1 ?

Dec 26, 2015

The solution for the system of equations is
color(blue)(x=139/17, y=(-59)/17

#### Explanation:

$3 x - y = 28$, multiplying this equation by $5$
$15 x - \textcolor{b l u e}{5 y} = 140$......equation $\left(1\right)$

$2 x + \textcolor{b l u e}{5 y} = - 1$.......equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$

$15 x - \cancel{\textcolor{b l u e}{5 y}} = 140$

$2 x + \cancel{\textcolor{b l u e}{5 y}} = - 1$

$17 x = 139$

color(blue)(x=139/17

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

$3 x - y = 28$

$3 \times \textcolor{b l u e}{\frac{139}{17}} - y = 28$

$\left(\frac{417}{17}\right) - y = 28$

$\left(\frac{417}{17}\right) - 28 = y$

$\left(\frac{417}{17}\right) - \frac{476}{17} = y$

color(blue)(y=-59/17