How do you use substitution to solve `3x - 2y = 2` and `x = 3y - 11`?

Substitution is done by choosing what variable has provided the easiest way to do the process. Since, the second equation `x=3y-11`; where value of x is already provided, it's convenient to solve the value of `y` first; that is,

`3x-2y=2->eq.1`
`x=3y-11->eq.2`

`3x-2y=2`
where `x=3y-11`, Now plug in the value of x

`3(3y-11)-2y=2`, distribution property

`9y-33-2y=2`, combine like terms

`9y-2y=2+33`, simplify the equation

`7y=35`. divide both sides by 7 to isolate the `y`

`(cancel(7)y)/cancel(7)=(cancel(35)5)/cancel(7)`

`y=5`

Now, find the value of `x` using the second equation and plug in the value of `y=5`:

`x=3y-11`

`x=3(5)-11`

`x=15-11`

`x=4`

Checking:

where: `x=4 "and " y=5`

`Eq.1:`
`3x-2y=2`
`3(4)-2(5)=2`
`12-10=2`
`2=2`

`Eq.2:`
`x=3y-11`
`4=3(5)-11`
`4=15-11`
`4=4`

You substitute the `x` with `3y-11` and keep simplifying until you get the answer. Here are the steps:

`3(3y-11)-2y=2`

(Then you distribute/ multiply 3 by what's inside the parentheses.)

`9y-33-2y=2`

(It may seem like you have your answer, but not yet! Hmm... it seems like there are two "y's", huh?)

`7y-33`

(I just did `9y-7y`)

`7y-33` is the answer.

My source is my knowledge.
I hope that helped you!