Question 200526

Start with the given system of equations:

{{{system(4x+y=16,4x+y=12)}}}



{{{-1(4x+y)=-1(16)}}} Multiply the both sides of the first equation by -1.



{{{-4x-y=-16}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-4x-1y=-16,4x+y=12)}}}



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-y)+(4x+y)=(-16)+(12)}}}



{{{(-4x+4x)+(-y+y)=-16+12}}} Group like terms.



{{{0x+0y=-4}}} Combine like terms.



{{{0=-4}}}Simplify.



Since {{{0=-4}}} is <font size="4"><b>NEVER</b></font> true, this means that there are no solutions. 



So the system is inconsistent.