Question

for what value of k does the pair of equations given below has a unique solution 2x+4y=6 kx+4y=7​

Answer 1

Answer:

Except 2 every value of k has unique solution.

Step-by-step explanation:

According to the Question

It is given that the equation have unique solution.

Equation 1st = 2x+4y=6

➻ 2x+4y-6 = 0

where,

a₁ = 2 , b₁ = 4 & c₁ = -6

Equation 2nd = kx + 4y=7

➻ kx +4y-7=0

where,

a₂ = k , b₂ = 4 & c₂ = -7

As we know the condition for unique solution.

• a₁/a₂ ≠ b₁/b₂

substitute the value we get

➻ 2/k ≠4/4

➻ 2/k ≠ 1

➻ 2≠ k

➻ k ≠ 2

Except 2 every value is correct for k .

Answer 2

Step-by-step explanation:

We have,

=> 2x + 4y = 6 - (1)

=> kx + 4y = 7 - (2)

To find,

=> For what value of k does the pair of equations given below has a unique solution.

Solution,

From the first equation we have, (1):

• a₁ = 2 , b₁ = 4 , c₁ = -6

From the second equation we have, (2):

• a₂ = k , b₂ = 4 , c₂ = -7

We know,

Infinite solution:

• a₁/a₂ ≠ b₁/b₂

So we get,

• 2/k ≠ 4/4
• 2/k ≠ 1/1
• 2 ≠ k

∴ Every value for the equations is correct, except the value of 2 since 2 is not equal to k.

Learn more:

Infinite solution:

• a₁/a₂ = b₁/b₂ = c₁/c₂

No solution:

• a₁/a₂ = b₁/b₂ ≠ c₁/c₂