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Question
Show that the following equations are consistent: 2x + 3y + 4 = 0, x + 2y + 3 = 0, 3x + 4y + 5 = 0
Sum
Solution
Given equations are
2x + 3y + 4 = 0
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(– 2) – 3(–4) + 4(– 2)
= – 4 + 12 – 8
= 0
∴ The given equations are consistent.
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Application of Determinants - Consistency of Three Linear Equations in Two Variables
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