Question

For what value of k the following system of equations have unique solution 2x+ky=1; 3x-5y=7.

Answer 1

k is not equal to -10/3
Method is attached.

Answer 2

Answer:

We have been given two equations 2x + ky = 11 & 3x - 5y = 7.

∴ We have to find a unique Solution for system of equation.

(i)For Unique solution, We have:-

• a1/a2 ≠ b1/b2

Here, a1 = 2 ,b1 = k & a2= 3 , b2 = 5

Substitute obtained values in Equation:

⇒ a1/a2 ≠ b1/b2

⇒ 2/3 ≠ k/-5

⇒ 3k≠ 10

∴ k = -10/3

(ii)For No Solution, We have:-

• a1/a2 = b1/b2 ≠ c1/c2

Here, a1 = 2 ,b1 = k & a2= 3 , b2 = - 5 & c1 = 11 , c2 = 7

Substitute obtained values in Equation:

⇒a1/a2 = b1/b2 ≠ c1/c2

⇒ 2/3 = k/-5 ≠ 11/7

⇒ 2/3 = k/-5

⇒ 3k = -10

⇒ k = -10/3

∴ k = -10/3