3x-2y=24 and 5x+6y=12

Question

i need to solve for x and y, how do i do that?

Answer 1

3x-2y=24 so 9x-6y=72 (multiply all numbers by 3), 6y=9x-72.

5x+6y=12 so 6y=12-5x, but 6y=9x-72, so:

9x-72=12-5x, 9x+5x=12+72=84, 14x=84, x=84/14=42/7=6. So x=6 and 6y=12-5x=12-30=-18, y=-18/6=-3; or 2y=3x-24=18-24=-6, so y=-6/2=-3. ANSWER: x=6, y=-3.

Another way: 3(3x-2y)=3×24, 9x-6y=72; and 5x+6y=12, so just add the two equations:

9x-6y+5x+6y=72+12=84, 9x+5x=14x=84, x=84/14=42/7=6. And then find y by substituting x=6 in either of the two original equations:

18-2y=24, 18-24=2y, -6=2y, -3=y, same as y=-3. ANSWER: x=6, y=-3.