Question 153565


Start with the given system of equations:

{{{system(5x-4y=1,-10x+8y=-3)}}}



{{{2(5x-4y)=2(1)}}} Multiply the both sides of the first equation by 2.



{{{10x-8y=2}}} Distribute and multiply.



So we have the new system of equations:

{{{system(10x-8y=2,-10x+8y=-3)}}}



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



{{{(10x-8y)+(-10x+8y)=(2)+(-3)}}}



{{{(10x+-10x)+(-8y+8y)=2+-3}}} Group like terms.



{{{0x+0y=-1}}} Combine like terms. Notice how the x terms cancel out.



{{{0=-1}}}Simplify.



Since {{{0=-1}}} is <font size="4"><b>never</b></font> true, this means that there are no solutions. So the system is inconsistent.