Question 554702

Start with the given system of equations:

{{{system(7x+2y=10,-7x+y=-17)}}}



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



{{{(7x+2y)+(-7x+y)=(10)+(-17)}}}



{{{(7x+-7x)+(2y+1y)=10+-17}}} Group like terms.



{{{0x+3y=-7}}} Combine like terms.



{{{3y=-7}}} Simplify.



{{{y=(-7)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



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{{{7x+2y=10}}} Now go back to the first equation.



{{{7x+2(-7/3)=10}}} Plug in {{{y=-7/3}}}.



{{{7x-14/3=10}}} Multiply.



{{{3(7x-14/cross(3))=3(10)}}} Multiply both sides by the LCD {{{3}}} to clear any fractions.



{{{21x-14=30}}} Distribute and multiply.



{{{21x=30+14}}} Add {{{14}}} to both sides.



{{{21x=44}}} Combine like terms on the right side.



{{{x=(44)/(21)}}} Divide both sides by {{{21}}} to isolate {{{x}}}.



So the solutions are {{{x=44/21}}} and {{{y=-7/3}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{44}{21},-\frac{7}{3}\right)].



This means that the system is consistent and independent.



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