Question 180713


Start with the given system of equations:

{{{system(3x-11y=9,-9x+33y=-27)}}}



{{{3(3x-11y)=3(9)}}} Multiply the both sides of the first equation by 3.



{{{9x-33y=27}}} Distribute and multiply.



So we have the new system of equations:

{{{system(9x-33y=27,-9x+33y=-27)}}}



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



{{{(9x-33y)+(-9x+33y)=(27)+(-27)}}}



{{{(9x+-9x)+(-33y+33y)=27+-27}}} Group like terms.



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



{{{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.