Question 236568


Start with the given system of equations:

{{{system(3x+4y=2,6x+8y=4)}}}



{{{-2(3x+4y)=-2(2)}}} Multiply the both sides of the first equation by -2.



{{{-6x-8y=-4}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-6x-8y=-4,6x+8y=4)}}}



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-8y)+(6x+8y)=(-4)+(4)}}}



{{{(-6x+6x)+(-8y+8y)=-4+4}}} 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.