Question 117988

Start with the given system

{{{-1x+2y=2}}}
{{{x=4-4y}}}




{{{-1(4-4y)+2y=2}}}  Plug in {{{x=4-4y}}} into the first equation. In other words, replace each {{{x}}} with {{{4-4y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{-4+4y+2y=2}}} Distribute



{{{6y-4=2}}} Combine like terms on the left side



{{{6y=2+4}}}Add 4 to both sides



{{{6y=6}}} Combine like terms on the right side



{{{y=(6)/(6)}}} Divide both sides by 6 to isolate y




{{{y=1}}} Divide





Now that we know that {{{y=1}}}, we can plug this into {{{x=4-4y}}} to find {{{x}}}




{{{x=4-4(1)}}} Substitute {{{1}}} for each {{{y}}}



{{{x=0}}} Simplify



So our answer is {{{x=0}}} and {{{y=1}}}