Question

Find the value of k for which the system of linear equations ax+ky=1/a and a^2cx+y=c have infinite solutions.

Answer 1

Answer:

$k=\frac{1}{ac}$

Step-by-step explanation:

Concept used:

If the system of equations

$a_1\:x+b_1\:y=c_1$

$a_2\:x+b_2\:y=c_2$ has infinitely many solutions , then

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

since the equations

$ax+ky=\frac{1}{a}$ and $a^2cx+y=c$ have inifinitely many solutioin,

$\frac{a}{a^2c}=\frac{k}{1}=\frac{\frac{1}{a}}{c}$

$\implies\frac{1}{ac}=\frac{k}{1}=\frac{1}{ac}$

$\implies\:k=\frac{1}{ac}$

Answer 2

Answer:

k =1/ac is the answer

Step-by-step explanation:

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