Question

Find the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 is inconsistent.

Answer 1

The given system is

x + 2y – 3 = 0                        ……(i)

5x + ky + 7 = 0                    ……(ii)

Here, `"a"_1 = 1, "b"_1 = 2, "c"_1 = -3, "a"_2 = 5, "b"_2 = "k" and "c"_2 = 7.`

For the system, to be inconsistent, we must have

`("a"_1)/("a"_2) =("b"_1)/("b"_2) ≠ ("c"_1)/("c"_2)`

`⇒ 1/5 = 2/"k" ≠ (−3)/7`

`⇒ 1/5 = 2/"k"`

⇒ k = 10

Hence, k = 10