Question 173339
{{{y=2x-2}}} Start with the first equation



{{{-x-1=2x-2}}} Plug in {{{y=-x-1}}}. In other words, replace "y" with x+1. What this does is eliminate the "y" term so we can solve for "x".



{{{-x=2x-2+1}}} Add {{{1}}} to both sides.



{{{-x-2x=-2+1}}} Subtract {{{2x}}} from both sides.



{{{-3x=-2+1}}} Combine like terms on the left side.



{{{-3x=-1}}} Combine like terms on the right side.



{{{x=(-1)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{x}}}.



{{{x=1/3}}} Reduce. So this is the first answer.



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Now that we know the value of "x", we can plug this value into either equation to find the value of "y".



{{{y=2x-2}}} Go back to the first equation



{{{y=2(1/3)-2}}} Plug in {{{x=1/3}}}



{{{y=2/3-2}}} Multiply



{{{y=-4/3}}} Combine like terms. This is our second answer.




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Answer:



So the solutions are {{{x=1/3}}} and {{{y=-4/3}}} which form the ordered pair *[Tex \LARGE \left(\frac{1}{3},-\frac{4}{3}\right)]



Since we have a unique solution, this means that the system is consistent and independent.