Solve by elimination

5x-y=12

3x+2y=2

(2) 5x-y=12

3x+2y=2

10x-2y=12

3x+2y=2

13x=2

x=0.15

Eliminate y

time first equation by 2 an add them together

10x-2y=24

3x+2y=2 +

13x+0y=26

13x=26

divide both sides by 13

x=2

sub back

3x+2y=2

3 (2) + 2y=2

6+2y=2

minus 6

2y=-4

divide 2

y=-2

(x, y)

(2,-2)