Question

How do you solve x=8-2y and x=-3y+12?

Answer 1

First solve for `y` using substitution, then solve for `x`, you will find that `y=4` and `x=0`

Explanation:

We're very lucky for this problem, as both expressions leave `x` by itself on one side. If you wanted to write this as one long expression:

`8-2y=x=-3y+12`

Now, we can ignore `x` and write the expression as follows (BECAUSE both expressions equal `x`):

`8-2y=-3y+12`

Since `x` is not in either equation, we can solve for `y` easily:

`cancel(8)-2ycolor(red)(+3y)color(blue)(cancel(-8))=cancel(-3y)+12color(red)(cancel(+3y))color(blue)(-8)`

`color(green)(y=4`

Finally, we can solve for `x`:

`x=8-2y`

`x=8-2(4)`

`x=8-8`

`color(green)(x=0)`

Answer 2

`(x,y)to(0,4)`

Explanation:

`x=8-2yto(1)`

`x=-3y+12to(2)`

`"since both equations express x in terms of y , equate"`
`"the right sides"`

`8-2y=-3y+12`

`"add "3y" to both sides"`

`8-2y+3y=12`

`"subtract 8 from both sides"`

`y=12-8=4`

`"substitute "y=4" into either of the 2 equations"`

`(1)tox=8-8=0`

`"the point of intersection "=(0,4)`
graph{(y+1/2x-4)(y+1/3x-4)=0 [-10, 10, -5, 5]}