Ex 4.6, 1 - Examine consistency x + 2y = 2, 2x + 3y = 3 - Checking consistency of equations

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  1. Chapter 4 Class 12 Determinants
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Ex 4.6, 1 Examine the consistency of the system of equations. x + 2y = 2 2x + 3y = 3 x + 2y = 2 2x + 3y = 3 Step 1 Write equation AX = B 1﷮2﷮2﷮3﷯﷯ 𝑥﷮𝑦﷯﷯ = 2﷮3﷯﷯ Hence A = 1﷮2﷮2﷮3﷯﷯, X = 𝑥﷮𝑦﷯﷯ & B = 2﷮3﷯﷯ Step 2 Calculate |A| |A| = 1﷮2﷮2﷮3﷯﷯ = 3 × 1 – 2 × 2 = 3 – 4 = – 1 ≠ 0 Since |A| ≠ 0 the system of equations is consistent

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