Question 114177

Start with the given system

{{{5x+5y=0}}}
{{{y=-3x-2}}}




{{{5x+5(-3x-2)=0}}}  Plug in {{{y=-3x-2}}} into the first equation. In other words, replace each {{{y}}} with {{{-3x-2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{5x+-15x-10=0}}} Distribute



{{{-10x-10=0}}} Combine like terms on the left side



{{{-10x=0+10}}}Add 10 to both sides



{{{-10x=10}}} Combine like terms on the right side



{{{x=(10)/(-10)}}} Divide both sides by -10 to isolate x




{{{x=-1}}} Divide





Now that we know that {{{x=-1}}}, we can plug this into {{{y=-3x-2}}} to find {{{y}}}




{{{y=-3(-1)-2}}} Substitute {{{-1}}} for each {{{x}}}



{{{y=1}}} Simplify



So our answer is {{{x=-1}}} and {{{y=1}}}