Find the value of k for system of equations has a unique solution:x +

1.	Find the value of k for system of equations has a unique solution:x + 2y = 3;5x + ky + 7 = 0
Answer» The given system of equations is: x + 2y – 3 = 0 5x + ky + 7 = 0 The above equations are of the form a₁ x + b₁ y − c₁ = 0 a₂ x + b₂ y − c₂ = 0 Here, a₁ = 1, b₁ = 2, c₁ = −3 a₂ = 5, b₂= k, c₂ = 7 So according to the question, For unique solution, the condition is \(\frac{a_1 }{a_2}\) ≠ \(\frac{b_1}{b_2}\) \(\frac{1}{5} ≠ \frac{2}{k}\) ⇒ k ≠ 10 Hence, the given system of equations will have unique solution for all real values of k other than 10.

Find the value of k for system of equations has a unique solution:x + 2y = 3;5x + ky + 7 = 0

Answer»

The given system of equations is:

x + 2y – 3 = 0

5x + ky + 7 = 0

The above equations are of the form

a₁ x + b₁ y − c₁ = 0

a₂ x + b₂ y − c₂ = 0

Here, a₁ = 1, b₁ = 2, c₁ = −3

a₂ = 5, b₂= k, c₂ = 7

So according to the question,

For unique solution, the condition is

\(\frac{a_1 }{a_2}\) ≠ \(\frac{b_1}{b_2}\)

\(\frac{1}{5} ≠ \frac{2}{k}\)

⇒ k ≠ 10

Hence, the given system of equations will have unique solution for all real values of k other than 10.