# How can one sixth x - 5 = one fifth x + 2 be set up as a system of equations?

6y - x = -30 and 5y - x = 10

5y + x = -30 and 5y + x = 10

6y - 6x = -30 and 5y - 5x = 10

5y + 5x = -30 and 5y + 5x = 10

**Solution:**

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

Consider y = 1/6 x - 5

Taking LCM

(x - 30)/6 = y

x - 30 = 6y

Using the subtraction property of equality

-30 = 6y - x

6y - x = -30

Again consider y = 1/5 x + 2

Taking LCM

(x + 10)/5 = y

By cross multiplication

x + 10 = 5y

Using the subtraction property of equality

5y - x = 10

Therefore, one sixth x - 5 = one fifth x + 2 can be set up as a system of equations as 6y - x = -30 and 5y - x = 10.

## How can one sixth x - 5 = one fifth x + 2 be set up as a system of equations?

**Summary:**

One sixth x - 5 = one fifth x + 2 can be set up as a system of equations as 6y - x = -30 and 5y - x = 10.

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