S =(-1, 2)
1) Solving this system by Elimination Method, we have to first decide what term should be eliminated first
x-y=-3
5x+3y=1
2) Let's eliminate y, by multiplying the 1st equation by 3
x-y=-3 x 3
5x+3y=1
3x-3y=-9 Add both equations simultaneously
5x+3y=1
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8x = -8 Divide both sides by 8
x=-1
3) Plug x=-1 into the first equation
x-y=-3
-1 -y = -3
- y = -3 +1
-y = -2
y= 2
Hence, the solution for that system is (-1, 2)