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Digiron [165]
3 years ago
13

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
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

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.

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