# How do you solve 3x + y = 2 and 4x + y = 20?

Oct 13, 2015

 color(green)(x = 18
 color(green)(y = -52

#### Explanation:

$3 x + y = 2$ --------(1)
$4 x + y = 20$------(2)

To eliminate $y$ we can subtract (1) from (2)

$\left(4 x + y\right) - \left(3 x + y\right) = 20 - 2$

$\left(4 x - 3 x\right) + \left(y - y\right) = 18$

 color(green)(x = 18

Substituting $x = 18$ in (1) we get

$3 \left(18\right) + y = 2$

$54 + y = 2$

Transposing 54 to the right hand side, we get

$y = 2 - 54$

 color(green)(y = -52