0.4x +3y = -45.5
-5x + 8y = -43
let's get rid of the decimal stuff
multiply the top equation by 50
20x +150y = -2275
-5x +8y = -43
multiply the bottom equation by 4
20x +150y = -2275
-20x +32y = -172
0x + 182y = -2447
182y = -2447
y = -2447/182
note: 2447 is a prime number, so it can't reduce.
now look at our equations:
20x +150y = -2275
-5x +8y = -43
multiply the top equation by 4
80x +600y = -9100
-5x +8y = -43
multiply the bottom equation by -75
80x +600y = -9100
375x -600y = 3225
add the equations together
455x +0y = -5875
455x = -5875
x = -5875/455
x = -1175/91
note: 1175 is 5*5*47 and 91 is 7*13, so nothing cancels
Answer: x = -1175/91, y = -2447/182