To solve the system using the elimination method (AKA combining the equations), you want to first set up the system so that one variable will be eliminated when you add the equations together.
The first equation has -2x, while the second one has -8x. If we multiply the entire first equation by -4, we'd turn that -2x into 8x, which would cancel out when you add that with the -8x in the second equation:
-4 ( -2x + y = 10 ) –> 8x - 4y = -40
-8x + 3y = 32 –> -8x + 3y = 32
And if you add the new equations on the right, you'll end up with
0x - y = -8
which means y = 8.
We could do the something similar to eliminate the y's. The first equation has y, while the second one has 3y. If we multiply the entire first equation by -3, we'd turn that y into -3y, which would cancel out when you add that with the 3y in the second equation:
-3 ( -2x + y = 10 ) –> 6x - 3y = -30
-8x + 3y = 32 –> -8x + 3y = 32
And if you add the new equations on the right, you'll end up with
-2x + 0y = 2
which means x = -1.
Putting those together, we have a solution of (-1, 8), which checks in both equations.