We are learning how to solve systems using elimination.

Question

2y - 1 = 3x - y / 5

3x - 4 / 8 = y/4

How would I begin to solve this? I'm mostly unsure of how to simplify the fractions. Thanks so much :)

Answer 1

2y - 1 = 3x - y/5
3x - 4/8 = y/4

First, simplify both equations
2y - 1 = 3x - y/5
Multiply both sides by 5
10y - 5 = 15x - y
11y - 15x = 5

3x - 4/8 = y/4
Multiply both sides by 8
24x - 4 = 2y
-2y + 24x = 4

Multiply by 2 (11y - 15x = 5)
Multiply by 11 (-2y + 24x = 4)

22y - 30x = 10
-22y + 264x = 44

Add equations
oy + 234x = 54
234x = 54
x = 54/234 = 3/13

Substitute x = 3/13 in either equation to find y.

Check your answer.
If you are correct, y = 10/13