Question 757428
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)

{{{25x-45y=-355}}}
{{{81x+45y=567}}}

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

{{{25x+81x = -355+567}}}
{{{106x = 212}}}
{{{x = 2}}}

Plug x back into one of the original equations to solve for y.
{{{9(2)+5y = 63}}}
{{{18 + 5y = 63}}}
{{{5y = 45}}}
{{{y = 9}}}