Question 218279


Start with the given system of equations:

{{{system(2x+y=-4,4x+2y=-8)}}}



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



{{{-4x-2y=8}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-4x-2y=8,4x+2y=-8)}}}



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



{{{(-4x-2y)+(4x+2y)=(8)+(-8)}}}



{{{(-4x+4x)+(-2y+2y)=8+-8}}} Group like terms.



{{{0x+0y=0}}} Combine like terms. Notice how the x terms cancel out.



{{{0=0}}}Simplify.



Since {{{0=0}}} is <font size="4"><b>always</b></font> true, this means that there are an infinite number of solutions. 



So the system is consistent and dependent.



Visually, this means that one graph is right on top of the other.