Question 365757


Start with the given system of equations:

{{{system(x+y=10,x-y=22)}}}



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)+(x-1y)=(10)+(22)}}}



{{{(1x+1x)+(1y+-1y)=10+22}}} Group like terms.



{{{2x+0y=32}}} Combine like terms.



{{{2x=32}}} Simplify.



{{{x=(32)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=16}}} Reduce.



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{{{x+y=10}}} Now go back to the first equation.



{{{16+y=10}}} Plug in {{{x=16}}}.



{{{y=10-16}}} Subtract {{{16}}} from both sides.



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



So the solutions are {{{x=16}}} and {{{y=-6}}}.



Which form the ordered pair *[Tex \LARGE \left(16,-6\right)].



This means that the system is consistent and independent.



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