Question 201105


Start with the given system of equations:

{{{system(-x+6y=3,3x-2y=5)}}}



{{{3(-x+6y)=3(3)}}} Multiply the both sides of the first equation by 3.



{{{-3x+18y=9}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-3x+18y=9,3x-2y=5)}}}



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



{{{(-3x+18y)+(3x-2y)=(9)+(5)}}}



{{{(-3x+3x)+(18y-2y)=9+5}}} Group like terms.



{{{0x+16y=14}}} Combine like terms.



{{{16y=14}}} Simplify.



{{{y=(14)/(16)}}} Divide both sides by {{{16}}} to isolate {{{y}}}.



{{{y=7/8}}} Reduce.



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{{{-3x+18y=9}}} Now go back to the first equation.



{{{-3x+18(7/8)=9}}} Plug in {{{y=7/8}}}.



{{{-3x+63/4=9}}} Multiply.



{{{4(-3x+63/cross(4))=4(9)}}} Multiply both sides by the LCD {{{4}}} to clear any fractions.



{{{-12x+63=36}}} Distribute and multiply.



{{{-12x=36-63}}} Subtract {{{63}}} from both sides.



{{{-12x=-27}}} Combine like terms on the right side.



{{{x=(-27)/(-12)}}} Divide both sides by {{{-12}}} to isolate {{{x}}}.



{{{x=9/4}}} Reduce.



So the solutions are {{{x=9/4}}} and {{{y=7/8}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{9}{4},\frac{7}{8}\right)].



This means that the system is consistent and independent.