Question

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

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

INTERSECTING LINES?

Given, Pair of linear equation in two variables, We need to find the value of k for which the lines represented hy the given pair of linear equations will intersect at a unique point.

Compare each linear equation with the standard form of linear equation in two variables :-

⇒ ax + by + c = 0

Equations:

• kx - 2y = 3
• 3x + y = 5

On Comparing,

⇒ Equation 1:

• a1 = k
• b1 = -2
• c1 = 3

⇒ Equation 2:

• a2 = 3
• b2 = 1
• c2 = 5

For Unique solution, Following condition must be true:

⇒ ( a1 / a2 ) ≠ ( b1 / b2 )

⇒ k/3 ≠ -2/1

⇒ k ≠ -6

Here, Value of k can be anything except -6.

More Information :-

• For No solution ( Means, The lines are parallel to each other), Following condition must be true.

⇒ a1/a2 = b1/b2 ≠ c1/c2

• For Infinitely many solutions ( Means, The lines are coincident ), Following condition must be true.

⇒ a1/a2 = b1/b2 = c1/c2