4x+3y=19 and 6x-5y=-57
eliminate
multiply first equation by -6 and 2nd by 4
and add them
-24x-18y=-114
24x-20y=-228 +
0x-38y=-342
-38y=-342
divide both sides by -38
y=9
sub back
4x+3y=19
4x+3(9)=19
4x+27=19
minus 27 both sides
4x=-8
divide 4
x=-2
(x,y)
(-2,9)