# How do you solve the following system: 4x-5y= -1, -2x=6y+18 ?

Dec 31, 2015

The solution for the system of equations is
color(blue)(x=-96/34,y=-35/17

#### Explanation:

$\textcolor{b l u e}{4 x} - 5 y = - 1$........equation $1$

$- 2 x - 6 y = 18$, multiplying by $2$
$\textcolor{b l u e}{- 4 x} - 12 y = 36$........equation $2$

Solving by elimination.
Adding equations $1$ and $2$

$\textcolor{b l u e}{\cancel{4} x} - 5 y = - 1$

$\textcolor{b l u e}{\cancel{- 4 x}} - 12 y = 36$

$- 17 y = 35$

color(blue)(y=35/(-17)

Finding $x$ from equation $2$:

$- 2 x - 6 y = 18$

$- 2 x = 18 + 6 y$

$- 2 x = 18 + 6 \times \left(- \frac{35}{17}\right)$

$- 2 x = 18 - \frac{210}{17}$

$- 2 x = \frac{306}{17} - \frac{210}{17}$

$- 2 x = \frac{96}{17}$

$x = \frac{96}{17 \times - 2}$

color(blue)(x=96/(-34)