# How do you solve the system 14x+5y=31, 2x-3y=-29?

Jun 12, 2018

$y = 9 , x = - 1$

#### Explanation:

$\left(1\right) 14 x + 5 y = 31$
$\left(2\right) 2 x - 3 y = - 29$

Let's eliminate the y's the isolate the x and solve for x.
To do this, multiply (1) by 3, and (2) by 5.

$\left(1\right) 42 x + 15 y = 93$
$\left(2\right) 10 x - 15 y = - 145$

(1)+(2) to eliminate y.

This leaves us with:

$52 x = - 52$

therefore $x = - 1$

Substitute this back into one of the original equation to get:

$- 14 + 5 y = 31$
Solve for y,
$y = 9$