Question 369977

Start with the given system

{{{x+y=2}}}
{{{y=x+8}}}




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



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



{{{2x=2-8}}}Subtract 8 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=x+8}}} to find {{{y}}}




{{{y=(-3)+8}}} Substitute {{{-3}}} for each {{{x}}}



{{{y=5}}} Add



So our answer is {{{x=-3}}} and {{{y=5}}} which also looks like *[Tex \LARGE \left(-3,5\right)]



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Jim