Question

find k if x +2y = 5 3x + ky -15 = 0 has unique solution​

Answer 1

Answer:

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Answer 2

Solution:

Pre-Requisite: There are 3 conditions which give us an idea about the consistency of solutions in a pair of linear equations.

1. Unique Solution: If there are two equations:

• ax + by + c = 0 and px + qy + r = 0

Then, the condition for them to have unique solution is:

$\rightarrow \dfrac{a}{p} \neq \dfrac{b}{q} \neq \dfrac{c}{r}$

2. Infinite Solutions: Considering the same set of equations, the required condition is:

$\rightarrow \dfrac{a}{p} = \dfrac{b}{q} = \dfrac{c}{r}$

3. No Solutions: The required condition is:

$\rightarrow \dfrac{a}{p} = \dfrac{b}{q} \neq \dfrac{c}{r}$

According to the question, the given set of equations are:

• x + 2y = 5

• 3x + ky = 15

Hence we get:a = 1, b = 2, c = -5, p = 3, q = k, r = -15

Applying the condition for unique solution we get:

$\rightarrow \dfrac{1}{3} \neq \dfrac{2}{k} \neq \dfrac{-5}{-15}\\\\\rightarrow \dfrac{2}{k} \neq \dfrac{1}{3}\\\\\rightarrow k \neq 6$

Hence for all values except 6, the given pair of equations will have a unique solution.