Solve each system of equations by adding, subtracting, or multiplying. 3) 5x + y = 9 10x - 7y = -18 show your work!

First we want to isolate x from 5x + y = 9 so to do so. We subtract y from both sides.
5x + y - y = 9 - y
Simplify.
5x = 9 - y
Divide both sides by 5.
5x/5 = 9/5 - y/5
Simplify again.
x = 9 - 5/y
Substitute x = 9 - 5/y
So 10 * 9 - 5/y - 7y = -18.
We wanna isolate y so...
10 * 9 - 5/y
Multiply the fractions.
(9 - y) * 10/5
Divide the numbers (10/5 = 2)
2(-y + 9)
Now we want to expand this.
2 * 9 + 2(-y)
Apply the minusplus rule
2 * 9 - 2y
This gives us 18 - 2y
From there we can add the similar elements
-2y - -7y = -9y
18 - 9y = -18
Subtract 18 from both sides.
18 - 9y - 18 = -18 - 18
Simplify again.
-9y = -36
Now divide both sides by -9
-9y/-9 = -36/-9
This gives us y = 4.
For x we just want to substitute 4 into it. 
So 9 - 4/5 which is 5/5 which translates to 1.
Therefore y = 4 and x = 1.