Q. 134.4( 5 Votes )

Find the value of k for which the system of equations 3x + y = 1 and kx + 2y = 5 has (i) a unique solution, (ii) no solution.

Class 10th RS Aggarwal - Mathematics 3. Linear Equations in Two Variables

Answer :

The given system of equations is 3x + y = 1 and kx + 2y = 5.

We know that the general form for a pair of linear equations in 2 variables x and y is a₁x + b₁y + c₁ = 0

and a₂x + b₂y + c₂ = 0.

Comparing with above equations,

we have a₁ = 3, b₁ = 1, c₁ = - 1; a₂ = k, b₂ = 2, c₂ = - 5

i) For the given system of equations to have a unique solution,

⇒

⇒ k ≠ 6

For k ≠ 6, the given system of equations has a unique solution.

ii) For the given system of equations to have no solution,

⇒

⇒ k = 6

For k = 6, the given system of equations has no solution.

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