Question 172785

As the name implies, substitution simply involves you "substituting" one variable in for another so that you can solve for that variable.

Let's solve the given system by substitution

{{{x-4y=-12}}}
{{{y=-4+2x}}}

{{{x-4(-4+2x)=-12}}}  Plug in {{{y=-4+2x}}} into the first equation. In other words, replace each {{{y}}} with {{{-4+2x}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.

{{{x+16-8x=-12}}} Distribute

{{{-7x+16=-12}}} Combine like terms on the left side

{{{-7x=-12-16}}}Subtract 16 from both sides

{{{-7x=-28}}} Combine like terms on the right side

{{{x=(-28)/(-7)}}} Divide both sides by -7 to isolate x

{{{x=4}}} Divide

Now that we know that {{{x=4}}}, we can plug this into {{{y=-4+2x}}} to find {{{y}}}

{{{y=-4+2(4)}}} Substitute {{{4}}} for each {{{x}}}

{{{y=4}}} Simplify

So our answer is {{{x=4}}} and {{{y=4}}} which forms the ordered pair *[Tex \LARGE \left(4,4\right)]
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