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Question

Find k if the following system of equations has infinite solutions
kx + 3y = k - 3
12x + ky = k


Find k if the following system of equations has no solution
3x + 2y = 6
kx + (k - 1)y = 9

Submitted: 545 days and 17 hours ago.
Category: Math
Value: $9
Status: CLOSED

Accepted Answer

Find k if the following system of equations has infinite solutions
kx + 3y = k - 3
12x + ky = k


we rewrite the equations to

y = (k/3)x + (k-3)/3

y = (12/k)x + k/k = (12/k)x + 1


We want infinite solutions, so the lines must coincide. In other words we want the slopes to be equal, and the intercept to be equal.

We want k/3 = 12/k and (k-3)/3 = 1. These conditions are satisfied for k = 6.


So k = 6.

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Find k if the following system of equations has no solution
3x + 2y = 6
kx + (k - 1)y = 9

We want the lines to be parallell, which is the same as having same coefficients:

If we set k = 3, we have:

3x + 2y = 6
3x + 2y = 9, and obviously the cannot be satisfied at the same time.

So k = 3.

Sincerely,
Sk1llz


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Expert: Sk1llz
Pos. Feedback: 100.0 %
Accepts: 
Answered: 5/26/2008

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Mathematics, Statistics and Physics

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