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Question
Answer the following question:
Find the value of k if the following equation are consistent:
(k − 2)x + (k − 1)y = 17 , (k − 1)x + (k − 2)y = 18 and x + y = 5
Solution
Since the given equations are consistent,
`|("k" - 2, "k" - 1, 17),("k" - 1, "k" - 2, 18),(1, 1, 5)|` = 0
By R2 – R1, we get,
`|("k" - 2, "k" - 1, 17),(1, -1, 1),(1, 1, 5)|` = 0
By C2 – C1, we get,
`|("k" - 2, 1, 17),(1, -2, 1),(1, 0, 5)|` = 0
∴ (k – 2)( –10 – 0) – 1(5 – 1) + 17(0 + 2) = 0
∴ - 10k + 20 – 4 + 34 =0
∴ -10k = – 50
∴ k = 5.
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