SOLUTION: Find K if the given system of equations has infinite no of solutions. 2x+ky=1+2y and kx+12y=3 (1)-4 (2)6 (3)Either (1) or (2) (4) none of these. i have chosen (3). But the

Question 146258: Find K if the given system of equations has infinite no of solutions.
2x+ky=1+2y and kx+12y=3
(1)-4 (2)6 (3)Either (1) or (2) (4) none of these.
i have chosen (3). But theanswer givenis (2). How it could be..?? plz explain this...??
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find K if the given system of equations has infinite no of solutions.
2x+ky=1+2y and kx+12y=3
(1)-4 (2)6 (3)Either (1) or (2) (4) none of these.
i have chosen (3). But the answer given is (2).
2x+ky = 1+2y
(k-2)y = 1-2x
y = (2x-1)/(2-k)
y = (2/2-k)x - 1/(2-k)
----------------
kx + 12y = 3
y = (-k/12)x + (1/4)
----------------
slopes and intercepts must be the same
2/(2-k) = -k/12
-1/(2-k) = 1/4
------------------
Solving the 2nd for "k" you get:
2-k = -4
k = 6
--------
And that works in the slopes equation.
--------------
Cheers,
Stan H.
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