Question 199797


Start with the given system of equations:

{{{system(9x+24y=90,3x+8y=30)}}}



{{{-3(3x+8y)=-3(30)}}} Multiply the both sides of the second equation by -3.



{{{-9x-24y=-90}}} Distribute and multiply.



So we have the new system of equations:

{{{system(9x+24y=90,-9x-24y=-90)}}}



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+24y)+(-9x-24y)=(90)+(-90)}}}



{{{(9x+-9x)+(24y+-24y)=90+-90}}} 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.



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