Question 172174


Start with the given system of equations:

{{{system(2x-9y=9,-18x+81y=-81)}}}



{{{9(2x-9y)=9(9)}}} Multiply the both sides of the first equation by 9.



{{{18x-81y=81}}} Distribute and multiply.



So we have the new system of equations:

{{{system(18x-81y=81,-18x+81y=-81)}}}



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



{{{(18x-81y)+(-18x+81y)=(81)+(-81)}}}



{{{(18x+-18x)+(-81y+81y)=81+-81}}} Group like terms.



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



{{{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.



Graphically, these two equations are really the SAME equation. So this means that there are an infinite number of intersections.