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?

Guest Oct 28, 2020

#1**+1 **

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!

Pangolin14 Oct 28, 2020