Question

(i) Write down the condition for which the following pair of linear equation will have
Infinitely many solution and find the value of k.
Kx + 2y = 5
4x + 8y = 20​

Answer 1

Question :-

• Write down the condition for which the following pair of linear equation will have Infinitely many solution and find the value of k.
• Kx + 2y = 5
• 4x + 8y = 20

Answer :-

Condition for the pair of lines having infinitely many solutions :-

Let consider pair of lines as

$\bf \: \: a_1 x + b_1 y + c_1 = 0 \: and \: a_2 x + b_2y + c_2 = 0.$

Then, system of equations have infinitely many solutions iff

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

Now, pair of equations are

Kx + 2y = 5

4x + 8y = 20

Here,

$\bf \:a_1 = k , \: b_1 = 2 , \: c_1 = 5$

$\bf \:a_2 = 4 , \: b_2 = 8 , \: c_2 = 20$

Now, these pair of equations have infinitely many solutions.

$\bf\implies \:\dfrac{k}{4} = \dfrac{2}{8} = \dfrac{5}{20}$

Taking first and second pair, we get

$\bf\implies \:\dfrac{k}{4} = \dfrac{2}{8}$

$\bf\implies \:\dfrac{k}{4} = \dfrac{1}{4}$

$\bf\implies \:k = 1$

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Answer 2

Answer:

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