# How can one fifth x - 2 = one third x + 8 be set up as a system of equations?

5y - 5x =10 and 3y - 3x = 24

5y - 5x = -10 and 3y + 3x = 24

5y + x = -10 and 3y + x = 24

5y - x = -10 and 3y - x = 24

**Solution:**

Given:

One fifth x - 2 = one third x + 8

**Writing in numerical form as:**

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

**Equating both to y**

y = 1/5 x - 2

y = 1/3 x + 8

**Taking LCM**

y = 1/5 x - 2 = (x - 10)/5

5y = x - 10 --- (1)

y = 1/3 x + 8 = (x + 24)/3

**By cross multiplication**

3y = x + 24 ---(2)

So we get,

**5y - x = -10 and 3y - x = 24**

Therefore,

**one fifth x - 2 = one third x + 8 can be set up as a system of equations as 5y - x = -10 and 3y - x = 24.**

## How can one fifth x - 2 = one third x + 8 be set up as a system of equations?

**Summary:**

One fifth x - 2 = one third x + 8 can be set up as a system of equations as 5y - x = - 10 and 3y - x = 24.

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