# 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.

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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