4x+3y=-45.5 and =5x+8y=-43 use elimination method

Question

use elimination method show your work if infinite number of solutions state this

Answer 1

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