Question 168735

{{{x/3-y/2=3}}} Start with the first equation.



{{{6(x/cross(3))-6(y/cross(2))=6(3)}}} Multiply EVERY term by the LCD {{{6}}} to clear the fractions.



{{{2x-3y=18}}} Multiply and simplify



---------------------------------




{{{x/2+y/3=7/3}}} Move onto the second equation.



{{{6(x/cross(2))+6(y/cross(3))=6(7/cross(3))}}} Multiply EVERY term by the LCD {{{6}}} to clear the fractions.



{{{3x+2y=14}}} Multiply and simplify



-----------------------------



So we have the system of equations:


{{{system(2x-3y=18,3x+2y=14)}}}



{{{2(2x-3y)=2(18)}}} Multiply the both sides of the first equation by 2.



{{{4x-6y=36}}} Distribute and multiply.



{{{3(3x+2y)=3(14)}}} Multiply the both sides of the second equation by 3.



{{{9x+6y=42}}} Distribute and multiply.



So we have the new system of equations:

{{{system(4x-6y=36,9x+6y=42)}}}



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



{{{(4x-6y)+(9x+6y)=(36)+(42)}}}



{{{(4x+9x)+(-6y+6y)=36+42}}} Group like terms.



{{{13x+0y=78}}} Combine like terms. Notice how the y terms cancel out.



{{{13x=78}}} Simplify.



{{{x=(78)/(13)}}} Divide both sides by {{{13}}} to isolate {{{x}}}.



{{{x=6}}} Reduce.



------------------------------------------------------------------



{{{4x-6y=36}}} Now go back to the first equation.



{{{4(6)-6y=36}}} Plug in {{{x=6}}}.



{{{24-6y=36}}} Multiply.



{{{-6y=36-24}}} Subtract {{{24}}} from both sides.



{{{-6y=12}}} Combine like terms on the right side.



{{{y=(12)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{y}}}.



{{{y=-2}}} Reduce.



So our answer is {{{x=6}}} and {{{y=-2}}}.



Which form the ordered pair *[Tex \LARGE \left(6,-2\right)].