# How do solve the following linear system?:  4x+2y=6 , 3x + y = -20 ?

May 22, 2016

The solution for the system of equations is:

color(green)(x = -23

 color(green)(y =49

#### Explanation:

$4 x + \textcolor{b l u e}{2 y} = 6$..............equation $\left(1\right)$
$3 x + y = - 20$, multiplying by $2$

$6 x + \textcolor{b l u e}{2 y} = - 40$......equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from equation $1$:

$4 x + \cancel{\textcolor{b l u e}{2 y}} = 6$

$- 6 x - \cancel{\textcolor{b l u e}{2 y}} = 40$

$- 2 x = 46$

$x = \frac{46}{- 2}$

color(green)(x = -23

Finding $y$ from equation $2 :$
$3 x + y = - 20$

$y = - 20 - 3 x$

$y = - 20 - 3 \times \left(- 23\right)$

$y = - 20 + 69$

 color(green)(y =49