Question

How do you work x=2y-2 and 3y=x+6 as substitution?

Answer 1

`=>x = 6`
`=>y = 4`

Explanation:

Substitution involves putting a known variable expression into another expression.

In this case, you are given `x = 2y-2`. You can substitute this into the second equation as follows:

`=>3y = x+6`

`=>3y = (2y-2) + 6`

`=>3y = 2y + 4`

`=>y = 4`

Now, you can use this `y = 4` to find the value of `x`. Going back to our expression for `x`:

`=>x = 2y - 2`

`=>x = 2(4) -2`

`=>x = 8 - 2`

`=>x = 6`

So the solution is `x = 6` and `y = 4`.

Answer 2

`y=4`
`x=6`

Explanation:

`x=2y-2`
`3y=x+6`

The first one will be easiest to plug into the second, since it is already defined for `x`. So, we will be substituting the `x` in the second equation with the definition of `x` provided in the first.

`3y=(2y-2)+6`

The parenthesis do not prevent you from combining like terms. In this case, the `-2` and `6`.

`3y=2y+4`

`3y-2y=4`

`y=4`

Now plug the `y` in to the top problem to solve for `x`.

`x=2(4)-2`

`x=6`

Results: `y=4` and `x=6`

Answer 3

`x=6`
`y=4`

Explanation:

`x=2y-2`
`3y=x+6`

To solve for each variable through substitution we have to make one equation have only one variable in it (either `x` or `y`). In order to do this, we have to put one variable in terms of the other. This time we got lucky because the first equation already puts `x` in terms of `y`. We just have to plug in `2y-2` for `x` in the second equation.

`3y=x+6`

`3y=(2y-2)+6`

`3y=2y+4`

Subtract `2y` from each side

`y=4`

Now plug this value into one of the original equations to find `x`.

`x=2y-2`

`x=2(4)-2`

`x=8-2`

`x=6`

OR

`3y=x+6`

`3(4)=x+6`

`12=x+6`

`6=x`

Answer

`x=6`
`y=4`