Question

How can 1/2x - 5 = 1/3x + 6 be set up as a system of equations?

A: 2y+x = -10
3y+x = 18

B: 2y+2x = -10
3y+3x = 18

C: 2y-x = -10
3y-x=18

D: 2y-2x = -10
3y-3x= 18

Answer 1

y = 1/2x - 5...2y = x - 10...2y - x = -10
y = 1/3x + 6....3y = x + 18...3y - x = 18
answer C

Answer 2

`2y - x = -10`

`3y-x=18`

Explanation:

Set up as a system of equation

`(1)/(2) x - 5 = (1)/(3) x + 6`

To get system of equations, we set each side of the given equation equals to y

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

Multiply whole equation by 2. That is we multiply each term by 2

`x - 10=2y`

Subtract x on both sides

`2y - x = -10` (first equation)

`y = (1)/(3) x + 6`

Multiply whole equaiton by 3

`3y=x +18`

Subtract x on both sides

`3y-x=18` (second equation)