# How do you solve the following system: 4x-5y-23=0 , -2x=6y+18 ?

Mar 30, 2016

$x = 1.41 , y = - 3.47$

#### Explanation:

For the first equation, start by adding $23$ to both sides, so that:

$4 x - 5 y = 23$

Then for the second equation, subtract $6 y$ from both sides, so that:

$- 2 x - 6 y = 18$

Then solve for $y$ by multiplying the second equation by $2$ on both sides and adding the two equations:

$4 x - 5 y = 23$
$+ 2 \cdot \left(- 2 x - 6 y\right) = 2 \cdot 18$

This gives:

$- 17 y = 59$, so $y = - 3.47$

Then, to solve for $x$, multiply both sides of the first equation by 6 and both sides of the second equation by $- 5$ and add them:

$6 \cdot \left(4 x - 5 y\right) = 6 \cdot 23$
$+ 5 \cdot \left(2 x - 6 y\right) = - 5 \cdot 18$

This gives:

$34 x = 48$, so $x = 1.41$

You can check your answers by substituting $1.41$ for $x$ and $- 3.47$ for $y$.