Question 147009


{{{(3/7)x+(5/9)y=27}}} Start with the first equation.



{{{63((3/cross(7))x+(5/cross(9))y)=63(27)}}} Multiply both sides by the LCD {{{63}}} to clear any fractions.



{{{27x+35y=1701}}} Distribute and multiply.




{{{(1/9)x+(2/7)y=7}}} Now move onto the next equation.



{{{63((1/cross(9))x+(2/cross(7))y)=63(7)}}} Multiply both sides by the LCD {{{63}}} to clear any fractions.



{{{7x+18y=441}}} Distribute and multiply.





Start with the given system of equations:

{{{system(27x+35y=1701,7x+18y=441)}}}



{{{-7(27x+35y)=-7(1701)}}} Multiply the both sides of the first equation by -7.



{{{-189x-245y=-11907}}} Distribute and multiply.



{{{27(7x+18y)=27(441)}}} Multiply the both sides of the second equation by 27.



{{{189x+486y=11907}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-189x-245y=-11907,189x+486y=11907)}}}



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



{{{(-189x-245y)+(189x+486y)=(-11907)+(11907)}}}



{{{(-189x+189x)+(-245y+486y)=-11907+11907}}} Group like terms.



{{{0x+241y=0}}} Combine like terms. Notice how the x terms cancel out.



{{{241y=0}}} Simplify.



{{{y=(0)/(241)}}} Divide both sides by {{{241}}} to isolate {{{y}}}.



{{{y=0}}} Reduce.



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{{{-189x-245y=-11907}}} Now go back to the first equation.



{{{-189x-245(0)=-11907}}} Plug in {{{y=0}}}.



{{{-189x+0=-11907}}} Multiply.



{{{-189x=-11907}}} Remove any zero terms.



{{{x=(-11907)/(-189)}}} Divide both sides by {{{-189}}} to isolate {{{x}}}.



{{{x=63}}} Reduce.



So our answer is {{{x=63}}} and {{{y=0}}}.



Which form the ordered pair *[Tex \LARGE \left(63,0\right)].



This means that the two equations are consistent and independent.