Question

Solve By Substitution: (With explanation Please!)

-5x + y = -3
3x - 8y = 24

Answer 1

x = 0 , y = -3

Steps:

given:

-5x + y = -3

3x - 8y = 24

1st method

3x - 8y = 24

8y = 3x - 24

y = (3x - 24)/8

-5x + y = -3

-5x + (3x - 24)/8 = -3

(-40x + 3x - 24)/8 = -3

(-37x - 24)/8 = -3

(-37x - 24) = -3 × 8

-37x - 24 = -24

-37x = 24 - 24

-37x = 0

x = 0

2nd method

y - 5x = -3

y = 5x-3

3x - 8y = 24

3x - 8(5x-3) = 24

3x - 40x + 24 = 24

3x + 40x = 24 - 24

43x = 0

x = 0

Answer 2

-5x + y = -3....A

3x - 8y = 24...B

Solve A for y.

-5x + y = -3

y = 5x - 3

Plug into B to solve for x

3x - 8(5x-3) = 24

3x -40x + 24 = 24

-37x = 24 - 24

-37x = 0

x = 0/-37

x = 0

Now that we know x, plug the value of x into A or B (your choice) to find y.

I will use B.

3x - 8y = 24

3(0) - 8y = 24

0 - 8y = 24

-8y = 24

y = 24/-8

y = -3

Answer: x = 0, y = -3