how to solve system of linear equations by elimination

Say you have the system:2x + 7y = 43x + 5y = -5To 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 = 10From here, we can add both equations together and get:11y = 22y = 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) = 42x + 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.