Question 554865

Start with the given system of equations:

{{{system(-12x-3y=-15,4x+y=5)}}}



{{{3(4x+y)=3(5)}}} Multiply the both sides of the second equation by 3.



{{{12x+3y=15}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-12x-3y=-15,12x+3y=15)}}}



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



{{{(-12x-3y)+(12x+3y)=(-15)+(15)}}}



{{{(-12x+12x)+(-3y+3y)=-15+15}}} 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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