SOLUTION: Can you help me with this problem? x + 2y = 5 kx + 3y = 3 For the system to be independent the slopes must not be the same. Study the two equations and complete the fo

Algebra ->  Linear-equations -> SOLUTION: Can you help me with this problem? x + 2y = 5 kx + 3y = 3 For the system to be independent the slopes must not be the same. Study the two equations and complete the fo      Log On


   

Question 676784: Can you help me with this problem?
x + 2y = 5
kx + 3y = 3

For the system to be independent the slopes must not be the same. Study the two equations and complete the following inequality for the slopes.
− k/3=
Multiply both sides by −3.
k ≠
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x + 2y = 5
rearranged as
2y = -x + 5
y = %28-1%2F2%29x+%2B+%285%2F2%29 --> linear equation for this line
...
kx + 3y = 3
rearranged as
3y = -kx + 3
y = %28-k%2F3%29x+%2B+%283%2F3%29 --> linear equation for this line
...
Since the slopes cannot be the same, solve for k when they are set equal
%28-1%2F2%29=%28-k%2F3%29
cross multiply
-3 = -2k
k = 3%2F2 when the slopes are the same.
therefore,
k%3C%3E3%2F2
.....................
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