<PRE><B>Question 275008</B>


Start with the given system of equations:

{{{system(7x-4y=14,-7x+6y=11)}}}



Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(7x-4y)+(-7x+6y)=(14)+(11)}}}



{{{(7x+-7x)+(-4y+6y)=14+11}}} Group like terms.



{{{0x+2y=25}}} Combine like terms.



{{{2y=25}}} Simplify.



{{{y=(25)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



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{{{7x-4y=14}}} Now go back to the first equation.



{{{7x-4(25/2)=14}}} Plug in {{{y=25/2}}}.



{{{7x-50=14}}} Multiply.



{{{7x=14+50}}} Add {{{50}}} to both sides.



{{{7x=64}}} Combine like terms on the right side.



{{{x=(64)/(7)}}} Divide both sides by {{{7}}} to isolate {{{x}}}.



So the solutions are {{{x=64/7}}} and {{{y=25/2}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{64}{7},\frac{25}{2}\right)].



This means that the system is consistent and independent.


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