# Rewrite the equation 4(2x-3y)=5(x+3y) so that y is a function of x.

### 5 Answers | Add Yours

You need to open the brackets both sides such that:

`8x - 12y = 5x + 15y`

You need to isolate all terms in y to the left side and all terms in x to the right side such that:

`-12y - 15y = -8x + 5x`

`-27y = -3x`

Dividing by -27 both sides yields:

`y = (-3x)/-27 =gt y = x/9`

**Hence, you should write y as a function of x such that: `y = f(x) = x/9.` **

4(2x-3y)=5(x+3y)

8x-12y=5x+15y

8x-5x= 15y+12y

3x=27y

y=3x/27

simplify

y=x/9

4(2x-3y)=5(x+3y)

Distribute the 4 and the 5

8x-12y = 5x+15y

Move the like terms to the same side:

-15y-12y=-8x+5x

combine the terms:

-27y=-3x

divide by -27 as we are trying to get y alone:

y=-3x/-27

both 3 and 27 share the common factor of 3 so divide both by 3

y= x/9

4(2x-3y)=5(x+3y)

Expanding, we get:

8x-12y=5x+15y

Shifting all the y's to the left and x's to the right, we get:

-15y-12y=-8x+5x

-27y=-3x

y=(-3/-27)x

y=(1/9)x

4(2x-3y)=5(x+3y)

8x-12y=5x+15y

-5x+12y

3x=27y

/27

3/27x=y

y=x/9