How do you find an ordered pair for 3x - 4y = 18 and 5y = x - 28?

Solve for x in one equation in order to substitute it into the other equation and you'll work through to get (-2,-6)

Explanation:

$3 x - 4 y = 18$
$5 y = x - 28$

We can solve the 2nd equation for x, then substitute that into the first equation. So let's first take the 2nd equation:

$5 y = x - 28$

and add 28 to both sides to get:

$x = 5 y + 28$

We can now substitute that into the first equation:

$3 x - 4 y = 18$

$3 \left(5 y + 28\right) - 4 y = 18$

now let's solve for y:

$15 y + 84 - 4 y = 18$

$11 y = - 66$

$y = - 6$

We can now substitute in the y value into one of our equations to find the x value. I'm going to use

$x = 5 y + 28$

$x = 5 \left(- 6\right) + 28$

$x = - 2$

$3 x - 4 y = 18$

$3 \left(- 2\right) - 4 \left(- 6\right) = 18$

$- 6 + 24 = 18$ check!

$5 y = x - 28$

$5 \left(- 6\right) = \left(- 2\right) - 28$

$- 30 = - 2 - 28$ check!

So the final answer is (-2,-6)