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

By cross multiplication

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.

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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.