Question 309872


Start with the given system of equations:

{{{system(5x+5y=-13,7x-3y=11)}}}



{{{3(5x+5y)=3(-13)}}} Multiply the both sides of the first equation by 3.



{{{15x+15y=-39}}} Distribute and multiply.



{{{5(7x-3y)=5(11)}}} Multiply the both sides of the second equation by 5.



{{{35x-15y=55}}} Distribute and multiply.



So we have the new system of equations:

{{{system(15x+15y=-39,35x-15y=55)}}}



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



{{{(15x+15y)+(35x-15y)=(-39)+(55)}}}



{{{(15x+35x)+(15y+-15y)=-39+55}}} Group like terms.



{{{50x+0y=16}}} Combine like terms.



{{{50x=16}}} Simplify.



{{{x=(16)/(50)}}} Divide both sides by {{{50}}} to isolate {{{x}}}.



{{{x=8/25}}} Reduce.



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{{{15x+15y=-39}}} Now go back to the first equation.



{{{15(8/25)+15y=-39}}} Plug in {{{x=8/25}}}.



{{{24/5+15y=-39}}} Multiply.



{{{5(24/cross(5)+15y)=5(-39)}}} Multiply both sides by the LCD {{{5}}} to clear any fractions.



{{{24+75y=-195}}} Distribute and multiply.



{{{75y=-195-24}}} Subtract {{{24}}} from both sides.



{{{75y=-219}}} Combine like terms on the right side.



{{{y=(-219)/(75)}}} Divide both sides by {{{75}}} to isolate {{{y}}}.



{{{y=-73/25}}} Reduce.



So the solutions are {{{x=8/25}}} and {{{y=-73/25}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{8}{25},-\frac{73}{25}\right)].



This means that the system is consistent and independent.