Question 120666

{{{3x-y=-8}}}
{{{y=x-4}}}

{{{3x-(x-4)=-8}}}  Plug in {{{y=x-4}}} into the first equation. In other words, replace each {{{y}}} with {{{x-4}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.

{{{3x-x+4=-8}}} Distribute the negative

{{{2x+4=-8}}} Combine like terms on the left side

{{{2x=-8-4}}}Subtract 4 from both sides

{{{2x=-12}}} Combine like terms on the right side

{{{x=(-12)/(2)}}} Divide both sides by 2 to isolate x

{{{x=-6}}} Divide

Now that we know that {{{x=-6}}}, we can plug this into {{{y=x-4}}} to find {{{y}}}

{{{y=(-6)-4}}} Substitute {{{-6}}} for each {{{x}}}

{{{y=-10}}} Simplify

So our answer is {{{x=-6}}} and {{{y=-10}}} which also looks like *[Tex \LARGE \left(-6,-10\right)]

Notice if we graph the two equations, we can see that their intersection is at *[Tex \LARGE \left(-6,-10\right)]. So this verifies our answer.

{{{ graph( 500, 500, -10, 10, -12, 10, (-8-3x)/-1, x-4) }}} Graph of {{{3x-y=-8}}} (red) and {{{y=x-4}}} (green)