Question 109230
You set it up perfectly


Start with the given system

{{{x+2y=39}}}
{{{y=x+12}}}




{{{x+2(x+12)=39}}}  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.



{{{x+2x+24=39}}} Distribute



{{{3x+24=39}}} Combine like terms on the left side



{{{3x=39-24}}}Subtract 24 from both sides



{{{3x=15}}} Combine like terms on the right side



{{{x=(15)/(3)}}} Divide both sides by 3 to isolate x




{{{x=5}}} Divide





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




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



{{{y=17}}} Simplify



So our answer is {{{x=5}}} and {{{y=17}}}



So our two numbers are 5 and 17