Question 264737


Start with the given system of equations:

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



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



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



So we have the new system of equations:

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



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



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



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



{{{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.