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Question
Find k if the following equations are consistent:
2x + 3y - 2 = 0, 2x + 4y − k = 0, x − 2y + 3k =0
Solution
Given equations are
2x + 3y - 2 = 0,
2x + 4y − k = 0,
x − 2y + 3k =0.
Since these equations are consistent,
`|(2, 3, -2),(2, 4, -"k"),(1, -2, 3"k")|` = 0
∴ 2(12k – 2k) – 3(6k + k) – 2(– 4 – 4) = 0
∴ 2(10k) – 3(7k) – 2(– 8) = 0
∴ 20k – 21k + 16 = 0
∴ k = 16
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