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Question
Find k if the following equations are consistent:
kx + 3y + 1 = 0, x + 2y + 1 = 0, x + y = 0
Solution
Given equations are
kx + 3y + 1 = 0,
x + 2y + 1 = 0,
x + y = 0, i.e., x + y + 0 = 0.
Since these equations are consistent,
`|("k", 3, 1),(1, 2, 1),(1, 1, 0")|` = 0
∴ k(0 – 1) – 3(0 – 1) + 1(1 – 2) = 0
∴ k(–1) – 3(–1) + 1(–1) = 0
∴ – k + 3 – 1 = 0
∴ k = 2
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