Question 146585

Start with the given system of equations:

{{{system(2x+3y=1,4x+6y=2)}}}



{{{-2(2x+3y)=-2(1)}}} Multiply the both sides of the first equation by -2.



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



So we have the new system of equations:

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



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



{{{(-4x+4x)+(-6y+6y)=-2+2}}} 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 two equations are consistent and dependent.