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Which of the following pairs of linear equations is/are inconsistent?

A. x−y=8;3x−3y=16x - y = 8; 3x - 3y = 16

B. 3x+2y=5;2x−3y=7.3x + 2y = 5; 2x - 3y = 7.

C. 2x−2y−2=0;4x−4y−5=0.2x - 2y - 2 = 0; 4x - 4y - 5 = 0.

D. 2x−3y=8;4x−6y−5=92x - 3y = 8; 4x - 6y - 5 = 9

Solution

✅ Correct Option: 2

A pair is inconsistent when a1/a2=b1/b2≠c1/c2a_1/a_2 = b_1/b_2 \neq c_1/c_2.

A: 1/3=1/3≠8/161/3 = 1/3 \neq 8/16, inconsistent.

B: 3/2≠2/(−3)3/2 \neq 2/(-3), so it has a unique solution.

C: 2/4=2/4≠2/52/4 = 2/4 \neq 2/5, inconsistent.

D: rewriting gives 4x−6y=144x - 6y = 14, and 2/4=3/6≠8/142/4 = 3/6 \neq 8/14, inconsistent.

So A, C and D.

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