For what value of k do the equations kx – 2y = 3 and 3x + y = 5 represent two lines intersecting at a unique point?

Question

Philoid · Accepted Answer

We have,

kx – 2y – 3 = 0

And, 3x + y – 5 = 0

Here, a₁ = k, b₁ = – 2 and c₁ = – 3

a₂ = 3, b₂ = 1 and c₂ = – 5

∴

And,

We know that, for these graphs intersect at a unique point we must have:

Hence, the lines of the graph will intersect at all real values of k except – 6

Thus, option D is correct