Question 332066

Start with the given system of equations:

{{{system(4x-6y=-26,-2x+3y=13)}}}



{{{2(-2x+3y)=2(13)}}} Multiply the both sides of the second equation by 2.



{{{-4x+6y=26}}} Distribute and multiply.



So we have the new system of equations:

{{{system(4x-6y=-26,-4x+6y=26)}}}



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)=(-26)+(26)}}}



{{{(4x+-4x)+(-6y+6y)=-26+26}}} 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.