Question 551102

Start with the given system of equations:

{{{system(7x-8y=11,8x-7y=7)}}}



{{{7(7x-8y)=7(11)}}} Multiply the both sides of the first equation by 7.



{{{49x-56y=77}}} Distribute and multiply.



{{{-8(8x-7y)=-8(7)}}} Multiply the both sides of the second equation by -8.



{{{-64x+56y=-56}}} Distribute and multiply.



So we have the new system of equations:

{{{system(49x-56y=77,-64x+56y=-56)}}}



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



{{{(49x-56y)+(-64x+56y)=(77)+(-56)}}}



{{{(49x+-64x)+(-56y+56y)=77+-56}}} Group like terms.



{{{-15x+0y=21}}} Combine like terms.



{{{-15x=21}}} Simplify.



{{{x=(21)/(-15)}}} Divide both sides by {{{-15}}} to isolate {{{x}}}.



{{{x=-7/5}}} Reduce.



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



{{{49x-56y=77}}} Now go back to the first equation.



{{{49(-7/5)-56y=77}}} Plug in {{{x=-7/5}}}.



{{{-343/5-56y=77}}} Multiply.



{{{5(-343/cross(5)-56y)=5(77)}}} Multiply both sides by the LCD {{{5}}} to clear any fractions.



{{{-343-280y=385}}} Distribute and multiply.



{{{-280y=385+343}}} Add {{{343}}} to both sides.



{{{-280y=728}}} Combine like terms on the right side.



{{{y=(728)/(-280)}}} Divide both sides by {{{-280}}} to isolate {{{y}}}.



{{{y=-13/5}}} Reduce.



So the solutions are {{{x=-7/5}}} and {{{y=-13/5}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{7}{5},-\frac{13}{5}\right)].



This means that the system is consistent and independent.