Question 378720


Start with the given system of equations:

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



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



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



So we have the new system of equations:

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



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



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



{{{(-8x+8x)+(-10y+10y)=-10+10}}} 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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Jim