Question 241749
Start with the given system of equations:

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



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



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



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



{{{6x+0y=-3}}} Combine like terms.



{{{6x=-3}}} Simplify.



{{{x=(-3)/(6)}}} Divide both sides by {{{6}}} to isolate {{{x}}}.



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



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{{{2x-y=-4}}} Now go back to the first equation.



{{{2(-1/2)-y=-4}}} Plug in {{{x=-1/2}}}.



{{{-1-y=-4}}} Multiply.



{{{-y=-4+1}}} Add {{{1}}} to both sides.



{{{-y=-3}}} Combine like terms on the right side.



{{{y=(-3)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=3}}} Reduce.



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



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



This means that the system is consistent and independent.