Question

Find the value of for which the
system of equations have infinitely
n-Ky=2,
5
3x+6y=
5​

Answer 1

Answer: n = 6/5; K = - 12/5.

Explanation:

For infinitely many solutions,

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

So,

n/3 = - K/6 = 2/5

• So, n/3 = 2/5 or n = 6/5
• And, K = 2/5 × (- 6) = - 12/5.

More: Equations having infinitely many solutions or even a single solution are called consistent pairs. For those equations which have no solutions, it is called inconsistent pair.

• In case of no solution, $\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$.
• And in case of one solution, $\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$.