Question

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Answer this question :-

For what values of k is the system of equations
3x - 2(k - 1)y = 30 and
4x - 2y = 35 consistent.

A) 3/4
B) 7/4
C) 1/2
D) None of the above

Waiting for a good answer

Answer 1

Answer:

7/4

Step-by-step explanation:

Given pair of linear equations is:

⇒ 3x - 2(k - 1)y = 30.

⇒ 4x - 2y = 35.

On comparing with ax + by + c = 0, we get

⇒ a₁ = 3, b₁ = -2(k - 1), c₁ = -30

⇒ a₂ = 4, b₂ = -2, c₂ = -35.

We know that a system has unique solution when it is consistent.

⇒ a₁/a₂ ≠ b₁/b₂

⇒ 3/4 ≠ -2(k - 1)/-2

⇒ 3/4 ≠  (k - 1)

⇒ 3 ≠ 4(k - 1)

⇒ 3 ≠ 4k - 4

⇒ 7 ≠ 4k

⇒ k ≠ 7/4

Therefore, the value of k = 7/4.

Hope it helps!

Answer 2

Answer:

7/4

Step-by-step explanation:

3x - 2(k - 1)y = 30.

4x - 2y = 35.

On comparing with ax + by + c = 0, we get

a₁ = 3, b₁ = -2(k - 1), c₁ = -30

a₂ = 4, b₂ = -2, c₂ = -35.

a₁/a₂ ≠ b₁/b₂

3/4 ≠ -2(k - 1)/-2

3/4 ≠  (k - 1)

3 ≠ 4(k - 1)

3 ≠ 4k - 4

7 ≠ 4k

k ≠ 7/4

k = 7/4.