Question 152569


Start with the given system of equations:

{{{system(-2x+y=1,-4x+2y=-8)}}}



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



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



So we have the new system of equations:

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



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-2y)+(-4x+2y)=(-2)+(-8)}}}



{{{(4x+-4x)+(-2y+2y)=-2+-8}}} Group like terms.



{{{0x+0y=-10}}} Combine like terms. Notice how the x terms cancel out.



{{{0=-10}}}Simplify.



Since {{{0=-10}}} is <font size="4"><b>never</b></font> true, this means that there are no solutions. So the system is inconsistent.