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Question
Answer the following question:
Find the value of k, if the following equations are consistent:
3x + y − 2 = 0 kx + 2y − 3 = 0 and 2x − y = 3
Solution
Given equations are
3x + y − 2 = 0,
kx + 2y − 3 = 0,
2x − y = 3, i.e., 2x − y − 3 = 0.
Since these equations are consistent,
`|(3, 1, -2),("k", 2, -3),(2, -1, -3)|` = 0
∴ 3(–6 – 3) –1(–3k + 6) –2(–k – 4) = 0
∴ 3(–9) – 1(–3k + 6) – 2(– k – 4) = 0
∴ –27 + 3k – 6 + 2k + 8 = 0
∴ 5k – 25 = 0
∴ k = `25/5`
= 5
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