Say you have the system:
2x + 7y = 4
3x + 5y = -5
To solve this system using elimination, you want to cancel out either the x terms or the y terms. In this equation, it makes most sense to get rid of the x terms because they can easily be calculated as opposites. So, what we need to do is multiply each term in the first equation by 3 and multiply each term in the second equation by -2:
6x + 21y = 12 (2 * 3 = 6; 7 * 3 = 21; 4 * 3 = 12)
-6x -10y = 10 (3 * -2 = -6; 5 * -2 = -10; -5 * -2 = 10)
With that, the x terms automatically cancel out and we're left with:
21y = 12
-10y = 10
From here, we can add both equations together and get:
11y = 22
y = 2 (divide both sides by 11)
After we have one variable, we can plug it right back into either of the first two original equations; ours were 2x + 7y = 4 and 3x + 5y = -5.
So we'll take the first one and put 2 in the place of y to solve for x:
2x + 7(2) = 4
2x + 14 = 4 (multiply 7 and 2)
2x = -10 (subtract 14 from both sides of the equation)
x = -5 (divide both sides by 2)
We have that y = 2 and x = -5; there is only one more step - check your work!
Plug both values back into both original equations to check your work:
2(-5) + 7(2) = 4 => -10 + 14 = 4 Correct!
3(-5) + 5(2) = -5 => -15 + 10 = -5 Correct!
I hope this was comprehensive enough. Let me know if you have any more questions.