Question 192045

Start with the given system of equations:

{{{system(5x+5y=-13,7x-2y=19)}}}



{{{2(5x+5y)=2(-13)}}} Multiply the both sides of the first equation by 2.



{{{10x+10y=-26}}} Distribute and multiply.



{{{5(7x-2y)=5(19)}}} Multiply the both sides of the second equation by 5.



{{{35x-10y=95}}} Distribute and multiply.



So we have the new system of equations:

{{{system(10x+10y=-26,35x-10y=95)}}}



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



{{{(10x+10y)+(35x-10y)=(-26)+(95)}}}



{{{(10x+35x)+(10y+-10y)=-26+95}}} Group like terms.



{{{45x+0y=69}}} Combine like terms.



{{{45x=69}}} Simplify.



{{{x=(69)/(45)}}} Divide both sides by {{{45}}} to isolate {{{x}}}.



{{{x=23/15}}} Reduce.



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{{{10x+10y=-26}}} Now go back to the first equation.



{{{10(23/15)+10y=-26}}} Plug in {{{x=23/15}}}.



{{{46/3+10y=-26}}} Multiply.



{{{cross(3)(46/cross(3))+3(10y)=3(-26)}}} Multiply EVERY term by the LCD {{{3}}} to clear any fractions.



{{{46+30y=-78}}} Multiply.



{{{30y=-78-46}}} Subtract {{{46}}} from both sides.



{{{30y=-124}}} Combine like terms on the right side.



{{{y=(-124)/(30)}}} Divide both sides by {{{30}}} to isolate {{{y}}}.



{{{y=-62/15}}} Reduce.



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Answer: 


So the solutions are {{{x=23/15}}} and {{{y=-62/15}}} 


which form the ordered pair *[Tex \LARGE \left(\frac{23}{15},-\frac{62}{15}\right)]