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Question
Examine the consistency of the following equation:
2x + 3y − 4 = 0, x + 2y = 3, 3x + 4y + 5 = 0
Solution
Given equations are
2x + 3y – 4 = 0,
x + 2y = 3, i.e., x + 2y – 3 = 0,
3x + 4y + 5 = 0.
`|(2, 3, -4),(1, 2, -3),(3, 4, 5)|`
= 2(10 + 12) – 3(5 + 9) – 4(4 – 6)
= 2(22) – 3(14) – 4(–2)
= 44 – 42 + 8
= 10 ≠ 0
∴ The given equations are not consistent.
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