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Question 472697: Given the system 2x+5y=1 and 3x+ky=4, find k such that this system has no solution.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Two linear equations will not intersect if they are parallel. The slope of the first line is -2/5 (simply solve for y), so we want the slope of the line 3x+ky = 4 to also equal -2/5.
Solving for y in the second equation we get y = (-3/k)x + (stuff), we set -3/k = -2/5 to get k = 15/2.
(The "stuff" indicates that it is not important so it is useless trying to find what its y-intercept is. It is only problematic when the y-intercepts of both equations are equal...in which they're not in this case)
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