# How do you find the solution of the system of equations 5x + 4y = 6 and -2x - 3y = -1?

Jun 20, 2018

Through elimination, we get:
$x = 2$
$y = - 1$

#### Explanation:

Manipulate the equations so that you can eliminate one of the variables. One possibility is to multiply the first equation by 2, and multiply the second equation by 5:

$+ 10 x + 8 y = 12$
$- 10 x - 15 y = - 5$

Then add the two equations together to eliminate $x$ and solve for $y$:
$0 - 7 y = 7$
$y = - 1$

Now substitute the value of $y$ into either of the original equations to find $x$:
$5 x + 4 y = 6$
$5 x + 4 \left(- 1\right) = 6$
$5 x = 6 + 4 = 10$
$x = 2$