Question

determine a and b for which two lines ax --2y=1 and 6x-4y=b have exactly one intersection point

Answer 1

There can be many values for a and b to have exactly one intersection point one of the values is a = 4 and b = 4

$\frac{a1}{a2} ≠\frac{b1}{b2}≠ \frac{c1}{c2}$

$\frac{4}{6} = \frac{2}{3} \: \\ \frac{2}{4} = \frac{1}{2} \\ \frac{1}{4} = \frac{1}{4} \\ \frac{2}{3} ≠ \frac{1}{2} ≠ \frac{1}{4}$

Answer 2

Answer:

a ≠ 3 b ∈ R

Step-by-step explanation:

Condition for intersection

m1 ≠ m2

$\frac{a1}{b1} ≠ \frac{a2}{b2}$

a/(-2) ≠ 6/(-4)

a ≠ 3

and b ∈ R

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