Question

For what value of k, the pair of equations 4x -3y =9, 2x + ky = 11 has no solution?

Answer 1

Answer:-

• 1st equation 4x -3y -9 = 0

• 2nd equation 2x +ky -11 = 0

where,

• a₁ = 4 , b₁ = -3 & c₁ = -9

• a₂ = 2 , b₂ = k & c₂ = -11

It is given that the pair of equation has no solution.

As we know that condition for no solution .

• a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Substitute the value we get

$:\implies$ 4/2 = -3/k ≠ -9/-11

$:\implies$ 2/1 = -3/k ≠ 9/11

$:\implies$ 2k = -3 × 1

$:\implies$ 2k = -3

$:\implies$ k = -3/2

• Hence, the value of k is -3/2 .

Answer 2

Given values,

4x -3y =9

2x + ky = 11

Conversion,

4x -3y - 9 = 0 --- (1)

2x + ky - 11 = 0 --- (2)

We have formula,

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Now from eq. (1) and (2),

→ 4/2 = -3/k ≠ -9/-11

→ 4/2 = -3/k

→ 2 = -3/k

→ [ k = -3/2 ]

The value of k is -3/2.