Question

Determine the value(s) of k such that the system of linear equations has the indicated number of solutions. (Enter your answers as a comma-separated list.) An infinite number of solutions

9x + ky = 24
kx + y = 8

Answer 1

Answer:

k=3

Step-by-step explanation:

The given system of equations are

$9x+ky=24$

$kx+y=8$

We need to find the value of k if the given system of equation have infinite number of solutions.

If two equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ have infinite number of solutions, then

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

Using this we get

$\dfrac{9}{k}=\dfrac{k}{1}=\dfrac{-24}{-8}$

$\dfrac{9}{k}=\dfrac{k}{1}=3$

$\dfrac{k}{1}=3$

$k=3$

Therefore, the value of k is 3.