Question 395302


Start with the given system of equations:

{{{system(-3x+3y=-20,2x-3y=7)}}}



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



{{{(-3x+3y)+(2x-3y)=(-20)+(7)}}}



{{{(-3x+2x)+(3y+-3y)=-20+7}}} Group like terms.



{{{-x+0y=-13}}} Combine like terms.



{{{-x=-13}}} Simplify.



{{{x=(-13)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=13}}} Reduce.



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{{{-3x+3y=-20}}} Now go back to the first equation.



{{{-3(13)+3y=-20}}} Plug in {{{x=13}}}.



{{{-39+3y=-20}}} Multiply.



{{{3y=-20+39}}} Add {{{39}}} to both sides.



{{{3y=19}}} Combine like terms on the right side.



{{{y=(19)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



So the solutions are {{{x=13}}} and {{{y=19/3}}}.



Which form the ordered pair *[Tex \LARGE \left(13,\frac{19}{3}\right)].



This means that the system is consistent and independent.



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Jim