SOLUTION: Find k if the following system of equations has infinite solutions kx + 3y = k – 3 12x + ky = k

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Question 74209: Find k if the following system of equations has infinite solutions
kx + 3y = k – 3
12x + ky = k

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
If we let k=6 then we get
6x%2B3y=3
12x%2B6y=6
Notice how the 2nd equation is just two times the first equation (ie 2%286x%2B3y%29=2%283%29 becomes 12x%2B6y=6) Since one equation is a multiple of the other and the system is dependent, there are infinite solutions. In other words, the two equations produce the same line, but one equation is just twice the other.