Question 530986
 

Start with the given system of equations:

{{{system(x+y=6,x-y=-9)}}}



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)=(6)+(-9)}}}



{{{(1x+1x)+(1y+-1y)=6+-9}}} Group like terms.



{{{2x+0y=-3}}} Combine like terms.



{{{2x=-3}}} Simplify.



{{{x=(-3)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



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{{{x+y=6}}} Now go back to the first equation.



{{{-3/2+y=6}}} Plug in {{{x=-3/2}}}.



{{{2(-3/cross(2)+y)=2(6)}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{-3+2y=12}}} Distribute and multiply.



{{{2y=12+3}}} Add {{{3}}} to both sides.



{{{2y=15}}} Combine like terms on the right side.



{{{y=(15)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



So the solutions are {{{x=-3/2}}} and {{{y=15/2}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{3}{2},\frac{15}{2}\right)].



This means that the system is consistent and independent.



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