Question 176207


Start with the given system of equations:

{{{system(-6x+y=0,9x-12y=2)}}}



{{{12(-6x+y)=12(0)}}} Multiply the both sides of the first equation by 12.



{{{-72x+12y=0}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-72x+12y=0,9x-12y=2)}}}



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



{{{(-72x+12y)+(9x-12y)=(0)+(2)}}}



{{{(-72x+9x)+(12y+-12y)=0+2}}} Group like terms.



{{{-63x+0y=2}}} Combine like terms.



{{{-63x=2}}} Simplify.



{{{x=(2)/(-63)}}} Divide both sides by {{{-63}}} to isolate {{{x}}}.



{{{x=-2/63}}} Reduce.



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{{{-72x+12y=0}}} Now go back to the first equation.



{{{-72(-2/63)+12y=0}}} Plug in {{{x=-2/63}}}.



{{{16/7+12y=0}}} Multiply.



{{{7(16/cross(7)+12y)=7(0)}}} Multiply both sides by the LCD {{{7}}} to clear any fractions.



{{{16+84y=0}}} Distribute and multiply.



{{{84y=0-16}}} Subtract {{{16}}} from both sides.



{{{84y=-16}}} Combine like terms on the right side.



{{{y=(-16)/(84)}}} Divide both sides by {{{84}}} to isolate {{{y}}}.



{{{y=-4/21}}} Reduce.



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Answer:


So the solutions are {{{x=-2/63}}} and {{{y=-4/21}}}



which form the ordered pair *[Tex \LARGE \left(-\frac{2}{63},-\frac{4}{21}\right)]