Question 597795


Start with the given system of equations:

{{{system(5x+2y=8,7x+8y=3)}}}



{{{-4(5x+2y)=-4(8)}}} Multiply the both sides of the first equation by -4.



{{{-20x-8y=-32}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-20x-8y=-32,7x+8y=3)}}}



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



{{{(-20x-8y)+(7x+8y)=(-32)+(3)}}}



{{{(-20x+7x)+(-8y+8y)=-32+3}}} Group like terms.



{{{-13x+0y=-29}}} Combine like terms.



{{{-13x=-29}}} Simplify.



{{{x=(-29)/(-13)}}} Divide both sides by {{{-13}}} to isolate {{{x}}}.



{{{x=29/13}}} Reduce.



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{{{-20x-8y=-32}}} Now go back to the first equation.



{{{-20(29/13)-8y=-32}}} Plug in {{{x=29/13}}}.



{{{-580/13-8y=-32}}} Multiply.



{{{13(-580/cross(13)-8y)=13(-32)}}} Multiply both sides by the LCD {{{13}}} to clear any fractions.



{{{-580-104y=-416}}} Distribute and multiply.



{{{-104y=-416+580}}} Add {{{580}}} to both sides.



{{{-104y=164}}} Combine like terms on the right side.



{{{y=(164)/(-104)}}} Divide both sides by {{{-104}}} to isolate {{{y}}}.



{{{y=-41/26}}} Reduce.



So the solutions are {{{x=29/13}}} and {{{y=-41/26}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{29}{13},-\frac{41}{26}\right)].



This means that the system is consistent and independent.