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# How can one half x - 5 = one third x + 6 be set up as a system of equations?

**Solution:**

One half x - 5 = one third x + 6 [Given]

It can be mathematically written as

1/2 x - 5 = 1/3 x + 6

First rewrite it into two separate equations

y = 1/2 x - 5 … (1)

y = 1/3 x + 6 … (2)

Both the equations can be written as

equation (1):y = (x - 10)/2

2y = x - 10

**2y - x = - 10**

equation (2):y = (x + 18)/3

3y = x + 18

**3y - x = 18**

Therefore, one half x - 5 = one third x + 6 can be set up as a system of equations as 2y - x = -10 and 3y - x = 18.

## How can one half x - 5 = one third x + 6 be set up as a system of equations?

**Summary:**

One half x - 5 = one third x + 6 can be set up as a system of equations as 2y - x = -10 and 3y - x = 18.

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