Question 124700
Start with the given system

{{{2x-4y=18}}}
{{{y=-x-12}}}




{{{2x-4(-x-12)=18}}}  Plug in {{{y=-x-12}}} into the first equation. In other words, replace each {{{y}}} with {{{-x-12}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{2x+4x+48=18}}} Distribute



{{{6x+48=18}}} Combine like terms on the left side



{{{6x=18-48}}}Subtract 48 from both sides



{{{6x=-30}}} Combine like terms on the right side



{{{x=(-30)/(6)}}} Divide both sides by 6 to isolate x




{{{x=-5}}} Divide





Now that we know that {{{x=-5}}}, we can plug this into {{{y=-1x-12}}} to find {{{y}}}




{{{y=-(-5)-12}}} Substitute {{{-5}}} for each {{{x}}}



{{{y=-7}}} Simplify



So our answer is {{{x=-5}}} and {{{y=-7}}} which also looks like *[Tex \LARGE \left(-5,-7\right)]




Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-5,-7\right)]. So this verifies our answer.



{{{ graph( 500, 500, -10, 10, -10, 10, (18-2x)/(-4), -x-12) }}} Graph of {{{2x-4y=18}}} (red) and {{{y=-x-12}}} (green)