Question 146609

Start with the given system of equations:

{{{system(5x+5y=11,7x-3y=17)}}}



{{{3(5x+5y)=3(11)}}} Multiply the both sides of the first equation by 3.



{{{15x+15y=33}}} Distribute and multiply.



{{{5(7x-3y)=5(17)}}} Multiply the both sides of the second equation by 5.



{{{35x-15y=85}}} Distribute and multiply.



So we have the new system of equations:

{{{system(15x+15y=33,35x-15y=85)}}}



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)=(33)+(85)}}}



{{{(15x+35x)+(15y+-15y)=33+85}}} Group like terms.



{{{50x+0y=118}}} Combine like terms. Notice how the y terms cancel out.



{{{50x=118}}} Simplify.



{{{x=(118)/(50)}}} Divide both sides by {{{50}}} to isolate {{{x}}}.



{{{x=59/25}}} Reduce.



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{{{15x+15y=33}}} Now go back to the first equation.



{{{15(59/25)+15y=33}}} Plug in {{{x=59/25}}}.



{{{177/5+15y=33}}} Multiply.



{{{5(177/cross(5)+15y)=5(33)}}} Multiply both sides by the LCD {{{5}}} to clear any fractions.



{{{177+75y=165}}} Distribute and multiply.



{{{75y=165-177}}} Subtract {{{177}}} from both sides.



{{{75y=-12}}} Combine like terms on the right side.



{{{y=(-12)/(75)}}} Divide both sides by {{{75}}} to isolate {{{y}}}.



{{{y=-4/25}}} Reduce.



So our answer is {{{x=59/25}}} and {{{y=-4/25}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{59}{25},\frac{-4}{25}\right)].



This means that the two equations are consistent and independent.