Question 111721
Start with the given system

{{{3x+3y=6}}}
{{{y=-x+2}}}




{{{3x+3(-x+2)=6}}}  Plug in {{{y=-x+2}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{3x+-x+6=6}}} Distribute



{{{2x+6=6}}} Combine like terms on the left side



{{{2x=6-6}}}Subtract 6 from both sides



{{{2x=0}}} Combine like terms on the right side



{{{x=(0)/(2)}}} Divide both sides by 2 to isolate x




{{{x=0}}} Divide





Now that we know that {{{x=0}}}, we can plug this into {{{y=-x+2}}} to find {{{y}}}




{{{y=-(0)+2}}} Substitute {{{0}}} for each {{{x}}}



{{{y=2}}} Simplify



So our answer is {{{x=0}}} and {{{y=2}}}

So the system has one solution