Question 113902
Start with the given system

{{{x+y=-5}}}
{{{x=3y+7}}}




{{{(3y+7)+y=-5}}}  Plug in {{{x=3y+7}}} into the first equation. In other words, replace each {{{x}}} with {{{3y+7}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{3y+7+y=-5}}}



{{{4y+7=-5}}} Combine like terms on the left side



{{{4y=-5-7}}}Subtract 7 from both sides



{{{4y=-12}}} Combine like terms on the right side



{{{y=(-12)/(4)}}} Divide both sides by 4 to isolate y




{{{y=-3}}} Divide





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




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



{{{x=-2}}} Simplify



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