Question 161680


Start with the given system of equations:

{{{system(3x+2y=3,9x-8y=-2)}}}



{{{4(3x+2y)=4(3)}}} Multiply the both sides of the first equation by 4.



{{{12x+8y=12}}} Distribute and multiply.



So we have the new system of equations:

{{{system(12x+8y=12,9x-8y=-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:



{{{(12x+8y)+(9x-8y)=(12)+(-2)}}}



{{{(12x+9x)+(8y+-8y)=12+-2}}} Group like terms.



{{{21x+0y=10}}} Combine like terms. Notice how the y terms cancel out.



{{{21x=10}}} Simplify.



{{{x=(10)/(21)}}} Divide both sides by {{{21}}} to isolate {{{x}}}.



So the first part of the answer is {{{x=(10)/(21)}}}



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{{{12x+8y=12}}} Now go back to the first equation.



{{{12(10/21)+8y=12}}} Plug in {{{x=10/21}}}.



{{{40/7+8y=12}}} Multiply.



{{{7(40/cross(7)+8y)=7(12)}}} Multiply both sides by the LCD {{{7}}} to clear any fractions.



{{{40+56y=84}}} Distribute and multiply.



{{{56y=84-40}}} Subtract {{{40}}} from both sides.



{{{56y=44}}} Combine like terms on the right side.



{{{y=(44)/(56)}}} Divide both sides by {{{56}}} to isolate {{{y}}}.



{{{y=11/14}}} Reduce.



So the second part of the answer is {{{y=11/14}}}



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Answer:



So the solutions are {{{x=(10)/(21)}}} and {{{y=11/14}}} which forms the ordered pair *[Tex \LARGE \left(\frac{10}{21},\frac{11}{14}\right)]