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

A. x+y=5,2x+2y=10x + y = 5, 2x + 2y = 10

B. 2x+y−6=0,4x−2y−4=02x + y - 6 = 0, 4x - 2y - 4 = 0

C. x−y=8,3x−3y=16x - y = 8, 3x - 3y = 16

D. x−2y=0,3x+4y−20=0x - 2y = 0, 3x + 4y - 20 = 0

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 4

A: all three ratios are equal, so the lines coincide and there are infinitely many solutions, hence consistent.

B and D: the coefficient ratios differ, so the lines intersect once, hence consistent.

C: 13=−1−3≠816\frac{1}{3} = \frac{-1}{-3} \neq \frac{8}{16}, so the lines are parallel and the pair is inconsistent.

Hence A, B and D.

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