Question 325252

Start with the given system of equations:

{{{system(x-y=16,2x+y=2)}}}



Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(x-y)+(2x+y)=(16)+(2)}}}



{{{(x+2x)+(-y+y)=16+2}}} Group like terms.



{{{3x+0y=18}}} Combine like terms.



{{{3x=18}}} Simplify.



{{{x=(18)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=6}}} Reduce.



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{{{x-1y=16}}} Now go back to the first equation.



{{{6-1y=16}}} Plug in {{{x=6}}}.



{{{-y=16-6}}} Subtract {{{6}}} from both sides.



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



{{{y=(10)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=-10}}} Reduce.



So the solutions are {{{x=6}}} and {{{y=-10}}}.



Which form the ordered pair *[Tex \LARGE \left(6,-10\right)].



This means that the system is consistent and independent.