Question 677236


Start with the given system of equations:

{{{system(x+4y=-1,2x-4y=4)}}}



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



{{{(x+4y)+(2x-4y)=(-1)+(4)}}}



{{{(1x+2x)+(4y+-4y)=-1+4}}} Group like terms.



{{{3x+0y=3}}} Combine like terms.



{{{3x=3}}} Simplify.



{{{x=(3)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=1}}} Reduce.



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{{{x+4y=-1}}} Now go back to the first equation.



{{{1+4y=-1}}} Plug in {{{x=1}}}.



{{{4y=-1-1}}} Subtract {{{1}}} from both sides.



{{{4y=-2}}} Combine like terms on the right side.



{{{y=(-2)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



{{{y=-1/2}}} Reduce.



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



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



This means that the system is consistent and independent.