SOLUTION: Please help me solve this question. Find the value(s) of the constant k such that the system of linear equations: 9x + ky = 3, kx + y = 1 has (i) No solution. (ii) An infin

Question 1121330: Please help me solve this question.
Find the value(s) of the constant k such that the system of linear equations:
9x + ky = 3,
kx + y = 1
has
(i) No solution.
(ii) An infinite number of solutions.
(iii) Exactly one solution
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
write in slope-intercept form
the first is ky=-9x+3 or y=-(9/k)x+(3/k)
the second is y=-kx+1
The slopes are (-9/k) and -k.
For no or infinite solutions, the slopes are equal so set -9/k=-k
-k^2=-9
k=3 or -3
y=-3k+1
y=-3k+1
So for k=3, there are infinite solutions
try k=-3
y=3x-1
y=3x+1, there are no solutions (parallel lines)
For all other k, there is one solution.

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