SOLUTION: Please help me solve this equation using substitution 3y=x+6 x=2y-2

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Question 724359: Please help me solve this equation using substitution
3y=x+6
x=2y-2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Substitution means getting one of the equations to a form like
x = expression that does not include x
or
y = expression that does not include y,
and substituting the expression for the variable in the other equation.

In the case of system%283y=x%2B6%2Cx=2y-2%29 , the equation x=2y-2
already is in the form we want.
It says that x is equal to 2y-2 .
So we substitute the expression 2y-2 for x in 3y=x%2B6 to get
3y=2y-2%2B6 --> 3y=2y%2B4 --> 3y-2y=2y%2B4-2y --> highlight%28y=4%29

Now we got back to x=2y-2 and plug y=4 into it to find x:
x=2%284%29-2 --> x=4-2 --> highlight%28x=6%29

NOTES:
If none of the equation was in such a friendly form, we could convert it into the form we want.
For example, if we had system%283y=x%2B6%2C+4x%2B3y=21%29 ,
we would solve for x in 3y=x%2B6 because the x is not multiplied by anything other than 1, and that makes it easy.
3y=x%2B6 --> 3y-6=x%2B6-6 --> 3y-6=x <--> x=3y-6
If all the coefficients in front of x or y are number other than the usually omitted 1 and -1, solving for a variable gets ugly and we end up with fractions. In those cases, substitution may not be a good choice.