Question 148123
{{{x/4-y/11=-9/44}}} Start with the first equation.



{{{44(x/cross(4)-y/cross(11))=44(-9/cross(44))}}} Multiply both sides by the LCD {{{44}}} to clear any fractions.



{{{11x-4y=-9}}} Distribute and multiply.


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{{{x/6-y/13=-1/26}}} Move onto the second equation.



{{{78(x/cross(6)-y/cross(13))=78(-1/cross(26))}}} Multiply both sides by the LCD {{{78}}} to clear any fractions.



{{{13x-6y=-3}}} Distribute and multiply.




So now we have the system {{{system(11x-4y=-9,13x-6y=-3)}}}


Let's solve this system by use of elimination.



{{{6(11x-4y)=6(-9)}}} Multiply the both sides of the first equation by 6.



{{{66x-24y=-54}}} Distribute and multiply.



{{{-4(13x-6y)=-4(-3)}}} Multiply the both sides of the second equation by -4.



{{{-52x+24y=12}}} Distribute and multiply.



So we have the new system of equations:

{{{system(66x-24y=-54,-52x+24y=12)}}}



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



{{{(66x-24y)+(-52x+24y)=(-54)+(12)}}}



{{{(66x+-52x)+(-24y+24y)=-54+12}}} Group like terms.



{{{14x+0y=-42}}} Combine like terms. Notice how the y terms cancel out.



{{{14x=-42}}} Simplify.



{{{x=(-42)/(14)}}} Divide both sides by {{{14}}} to isolate {{{x}}}.



{{{x=-3}}} Reduce.



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{{{66x-24y=-54}}} Now go back to the first equation.



{{{66(-3)-24y=-54}}} Plug in {{{x=-3}}}.



{{{-198-24y=-54}}} Multiply.



{{{-24y=-54+198}}} Add {{{198}}} to both sides.



{{{-24y=144}}} Combine like terms on the right side.



{{{y=(144)/(-24)}}} Divide both sides by {{{-24}}} to isolate {{{y}}}.



{{{y=-6}}} Reduce.



So our answer is {{{x=-3}}} and {{{y=-6}}}.



Which form the ordered pair *[Tex \LARGE \left(-3,-6\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(-3,-6\right)]. So this visually verifies our answer.



{{{drawing(500,500,-13,7,-16,4,
grid(1),
graph(500,500,-13,7,-16,4,(-9-11x)/(-4),(-3-13x)/(-6)),
circle(-3,-6,0.05),
circle(-3,-6,0.08),
circle(-3,-6,0.10)
)}}} Graph of {{{11x-4y=-9}}} (red) and {{{13x-6y=-3}}} (green)