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If the equations 3x + 4y = 6 and 12x + k1y = k2 are parallel then what cannot be the value of k2. Also find the value of k1.

If the equations 3x + 4y = 6 and 12x + k1y = k2 are parallel then what cannot be the value of k2. Also find the value of k1. Correct Answer 24 and 16

Concept used:

For a pair of linear equation in two variables a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, the lines are:

Intersecting when a1/a2 ≠ b1/b2

Parallel when a1/a2 = b1/b2 ≠ c1/c2

Consistent when a1/a2 = b1/b2 = c1/c2

Calculation:

As the lines are parallel then, a1/a2 = b1/b2 ≠ c1/c2

⇒ 3/12 = 4/k1

⇒ k1 = 16

Also, 4/k1 ≠ −6/−k2

⇒ 4/16 ≠ 6/k2

∴ k2 ≠ 24 and k1 = 16

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