You can put this solution on YOUR website! To solve by elimination we first need to have the coefficients in front of one variable to be the same. For this problem I am going to eliminate y.
5x-9y=-71
9x+5y=63
5(5x-9y=-71)
9(9x+5y=63)
Now that the coefficients in front of the y's are the same I am going to add the two equations together because the signs in front of the coefficients are different (if they were the same we would need to subtract)
25x-45y=-355
+81x+45y=567
Plug x back into one of the original equations to solve for y.