Question 116202

Start with the given system

{{{4x+2y=8}}}
{{{y=-3x+7}}}




{{{4x+2(-3x+7)=8}}}  Plug in {{{y=-3x+7}}} into the first equation. In other words, replace each {{{y}}} with {{{-3x+7}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{4x+-6x+14=8}}} Distribute



{{{-2x+14=8}}} Combine like terms on the left side



{{{-2x=8-14}}}Subtract 14 from both sides



{{{-2x=-6}}} Combine like terms on the right side



{{{x=(-6)/(-2)}}} Divide both sides by -2 to isolate x




{{{x=3}}} Divide





Now that we know that {{{x=3}}}, we can plug this into {{{y=-3x+7}}} to find {{{y}}}




{{{y=-3(3)+7}}} Substitute {{{3}}} for each {{{x}}}



{{{y=-2}}} Simplify



So our answer is {{{x=3}}} and {{{y=-2}}}