Question 547475


Start with the given system of equations:

{{{system(2x+y=5,2x+y=1)}}}



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



{{{-2x-1y=-1}}} Distribute and multiply.



So we have the new system of equations:

{{{system(2x+y=5,-2x-1y=-1)}}}



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



{{{(2x+y)+(-2x-1y)=(5)+(-1)}}}



{{{(2x+-2x)+(1y+-1y)=5+-1}}} 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.