Question 218385


Start with the given system of equations:

{{{system(2x+y=10,6x+3y=30)}}}



{{{-3(2x+y)=-3(10)}}} Multiply the both sides of the first equation by -3.



{{{-6x-3y=-30}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-6x-3y=-30,6x+3y=30)}}}



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



{{{(-6x-3y)+(6x+3y)=(-30)+(30)}}}



{{{(-6x+6x)+(-3y+3y)=-30+30}}} 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.