4x +3y = -45.5
5x +8y = -43
multiply the top equation by 8
32x +24y = -364
5x +8y = -43
multiply the bottom equation by -3
32x +24y = -364
-15x -24y = 129
add the equations together
17x +0y = -235
17x = -235
x = -235/17
now look at the original equations
4x +3y = -45.5
5x +8y = -43
multiply the top equation by 5
20x +15y = -227.5
5x +8y = -43
multiply the bottom equation by -4
20x +15y = -227.5
-20x -32y = 172
add the equations together
0x -17y = -55.5
-17y = -55.5
-34y = -111
y = -111/-34
y = 111/34
Answer: x = -235/17, y = 111/34