Question

Find what value of k,for which the pair of given linear equation 3x+y-5=0 and kx-2y-4=0 has unique solution

Answer 1

Value of k,for which the pair of given linear equation 3x+y-5=0 and kx-2y-4=0 has unique solution

1.The given system of equations is:

kx - 2y – 4 = 0

3x + y – 5 = 0

2.The above equations are of the form

a1 x + b1 y − c1 = 0

a2 x + b2 y − c2 = 0

Here, a1 = k, b1 = -2, c1 = −4

a2 = 3, b2 = 1, c2 = -5

3. So according to the question,

For unique solution, the condition is

a1 / a2 ≠ b1 / b2

k/3 ≠ -2/1

⇒ k ≠ -6

4. Hence, the given system of equations will have unique solution for all real values of k other than -6