Question 190638


Start with the given system of equations:

{{{system(4x+5y=3,8x+10y=6)}}}



{{{-2(4x+5y)=-2(3)}}} Multiply the both sides of the first equation by -2.



{{{-8x-10y=-6}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-8x-10y=-6,8x+10y=6)}}}



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)=(-6)+(6)}}}



{{{(-8x+8x)+(-10y+10y)=-6+6}}} 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.