Question 807678
To solve a system of linear equations like {{{system(5x-9y=29,12x+y=47)}}}  by substitution,
we solve one equation for one variable,
and substitute the expression found for that variable into the other equation.


In the case of {{{system(5x-9y=29,12x+y=47)}}} , the easiest start is
to solve for {{{y}}} in {{{12x+y=47}}} .
{{{12x+y=47}}}
{{{y=47-12x}}}
Substituting {{{47-12x}}} for {{{y}}} in {{{5x-9y=29}}} we get
{{{5x-9(47-12x)=29}}}
{{{5x-423+108x=29}}}
{{{5x+108x=29+423}}}
{{{113x=452}}}
{{{x=452/113}}}
{{{highlight(x=4)}}}
Now, we plug that value into {{{y=47-12x}}} to find {{{y}}} :
{{{y=47-12*4}}}
{{{y=47-48}}}
{{{highlight(y=-1)}}}