Question 178512


Start with the given system of equations:

{{{system(4x-2y=-6,2x-y=-3)}}}



{{{-2(2x-y)=-2(-3)}}} Multiply the both sides of the second equation by -2.



{{{-4x+2y=6}}} Distribute and multiply.



So we have the new system of equations:

{{{system(4x-2y=-6,-4x+2y=6)}}}



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)=(-6)+(6)}}}



{{{(4x+-4x)+(-2y+2y)=-6+6}}} 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.