1.

Find the value of for which thesystem of equations have infinitelyn-Ky=2,53x+6y=5​

Answer»

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}.


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