Question 122925

Start with the given system

{{{3x-3y=-12}}}
{{{y=-3x-12}}}




{{{3x-3(-3x-12)=-12}}}  Plug in {{{y=-3x-12}}} into the first equation. In other words, replace each {{{y}}} with {{{-3x-12}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{3x+9x+36=-12}}} Distribute



{{{12x+36=-12}}} Combine like terms on the left side



{{{12x=-12-36}}}Subtract 36 from both sides



{{{12x=-48}}} Combine like terms on the right side



{{{x=(-48)/(12)}}} Divide both sides by 12 to isolate x




{{{x=-4}}} Divide





Now that we know that {{{x=-4}}}, we can plug this into {{{y=-3x-12}}} to find {{{y}}}




{{{y=-3(-4)-12}}} Substitute {{{-4}}} for each {{{x}}}



{{{y=0}}} Simplify



So our answer is {{{x=-4}}} and {{{y=0}}} which also looks like *[Tex \LARGE \left(-4,0\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-4,0\right)]. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (-12-3x)/(-3), -3x-12) }}} Graph of {{{3x-3y=-12}}} (red) and {{{y=-3x-12}}} (green)