Define one variable in terms of the other variable. For example:
-3x+y=19
y=3x+19
Then, plug that value into the other equation.
9x+7y=-47
9x+7(3x+19)=-47
Solve.
9x+21x+133=-47
30x+133=-47
30x=180
x=6
Plug that value back in to find the other variable.
-3x+y=19
-3(6)+y=19
-18+y=19
y=37
Solution: (6,37)