Question 557471

{{{system(9x+9y=54,9x-9y=-90)}}}

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

{{{(9x+9y)+(9x-9y)=(54)+(-90)}}}

{{{(9x+9x)+(9y+-9y)=54+-90}}} Group like terms.

{{{18x+0y=-36}}} Combine like terms.

{{{18x=-36}}} Simplify.

{{{x=(-36)/(18)}}} Divide both sides by {{{18}}} to isolate {{{x}}}.

{{{x=-2}}} Reduce.

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{{{9x+9y=54}}} Now go back to the first equation.

{{{9(-2)+9y=54}}} Plug in {{{x=-2}}}.

{{{-18+9y=54}}} Multiply.

{{{9y=54+18}}} Add {{{18}}} to both sides.

{{{9y=72}}} Combine like terms on the right side.

{{{y=(72)/(9)}}} Divide both sides by {{{9}}} to isolate {{{y}}}.

{{{y=8}}} Reduce.

So the solutions are {{{x=-2}}} and {{{y=8}}}.

Which form the ordered pair *[Tex \LARGE \left(-2,8\right)].

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(-2,8\right)]. So this visually verifies our answer.

{{{drawing(500,500,-12,8,-2,18,
grid(1),
graph(500,500,-12,8,-2,18,(54-9x)/(9),(-90-9x)/(-9)),
circle(-2,8,0.05),
circle(-2,8,0.08),
circle(-2,8,0.10)
)}}} Graph of {{{9x+9y=54}}} (red) and {{{9x-9y=-90}}} (green)

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