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# For a certain value of k

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For a certain value of k, the system
x + y + 3z = 10,
-4x + 3y + 6z = 8,
kx + z = 3
has no solutions.  What is this value of k?

Oct 28, 2020

#1
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First, we evaluate the result of the equations without k. We get:

$$y = 6 x - 12, z = 22/3 - (7 x)/3$$

$$x = 1/7 (22 - 3 z)$$

For $kx+z=3$ to agree with these equations, we need to solve for k.

Solving for k in terms of z, $$k = \frac{ 7 (z - 3)}{3 z - 22}.$$

However, we want $kx+z \ne 3.$

See if you can work more on this on your own!

Oct 28, 2020