Question 724359
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(3y=x+6,x=2y-2)}}} , 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+6}}} to get
{{{3y=2y-2+6}}} --> {{{3y=2y+4}}} --> {{{3y-2y=2y+4-2y}}} --> {{{highlight(y=4)}}}
 
Now we got back to {{{x=2y-2}}} and plug {{{y=4}}} into it to find {{{x}}}:
{{{x=2(4)-2}}} --> {{{x=4-2}}} --> {{{highlight(x=6)}}}
 
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(3y=x+6, 4x+3y=21)}}} ,
we would solve for {{{x}}} in {{{3y=x+6}}} because the x is not multiplied by anything other than 1, and that makes it easy.
{{{3y=x+6}}} --> {{{3y-6=x+6-6}}} --> {{{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.