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