. 4x + 3y = -45.5, -5x + 8y = -43

Question

need to use elimination method and show all work.

Answer 1

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