3x - 5y = 18 over
-10x + 5y = 10
Add them because the 5y's have the right symbols for us to add
-7x = 28
Divide
x = -4
Now you can plug in -4 for x in one equation, I would use the first equation!
3(-4) - 5y = 18
-12 - 5y = 18
Add 12
-5y = 30
Divide
y = -6
Your solutions are going to be:
x = -4
y = -6
To check your work plug x and y into one equation:
3(-4) - 5(-6) = 18
-12 + 30 = 18
18 = 18
Since 18 does equal 18 you know that your solution's work!