SOLUTION: Determine the value of k for which the system of linear equations 2x−y =5 6x+ky=2 Has no solution. k=?

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Question 649252: Determine the value of k for which the system of linear equations
2x−y =5
6x+ky=2
Has no solution.
k=?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Now we want a system with no solutions. This mean the slopes are the same,
but the y-intercepts are different,the lines are parallel . Again, let's get these into slop-intercept form.
2x-y+=5....->...y=2x-5
6x%2Bky=2...->....y=-%286%2Fk%29x%2B2%2Fk
Again, we set the slopes equal to each other. This gives us 2 = -(6/k).
2k+=+-6
k+=+-6%2F2
highlight%28k=-3%29
Now, we need to verify that the y-intercepts are not the same.
first substitute k in y=-%286%2Fk%29x%2B2%2Fk
y=-%286%2F-3%29x%2B2%2F-3
y=2x-2%2F3
The first one is -5, and the second one is 2%2Fk, or -2%2F3
They clearly are not the same, so the system+has+no+solutions.

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graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C0%2C2x-5%2C2x-2%2F3%29