Question 209718


Start with the given system of equations:

{{{system(4x+3y=4,6x-6y=-1)}}}



{{{2(4x+3y)=2(4)}}} Multiply the both sides of the first equation by 2.



{{{8x+6y=8}}} Distribute and multiply.



So we have the new system of equations:

{{{system(8x+6y=8,6x-6y=-1)}}}



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



{{{(8x+6y)+(6x-6y)=(8)+(-1)}}}



{{{(8x+6x)+(6y+-6y)=8+-1}}} Group like terms.



{{{14x+0y=7}}} Combine like terms.



{{{14x=7}}} Simplify.



{{{x=(7)/(14)}}} Divide both sides by {{{14}}} to isolate {{{x}}}.



{{{x=1/2}}} Reduce.



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{{{8x+6y=8}}} Now go back to the first equation.



{{{8(1/2)+6y=8}}} Plug in {{{x=1/2}}}.



{{{4+6y=8}}} Multiply.



{{{6y=8-4}}} Subtract {{{4}}} from both sides.



{{{6y=4}}} Combine like terms on the right side.



{{{y=(4)/(6)}}} Divide both sides by {{{6}}} to isolate {{{y}}}.



{{{y=2/3}}} Reduce.



So the solutions are {{{x=1/2}}} and {{{y=2/3}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{1}{2},\frac{2}{3}\right)].



This means that the system is consistent and independent.