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Solve the pair of linear equations 3p + 5q = 21 and 2p + q = 7 by the substitution method.

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p = 2, q = 3

p = 3, q = 2

p = 2, q = -3

p = -2, q = -3

answer is A.

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Detailed Solution

The pair of linear equations is given as:

3p + 5q = 21 ... (1)

2p + q = 7 ... (2)

From equation (2):

q = 7 − 2p ... (3)

Substituting the value of q in (1):

3p + 5(7 - 2p) = 21

3p + 35 - 10p = 21

-7p = -14

p = 2

Substituting p = 2 in (3):

q = 7 − 2 (2) = 7 − 4 = 3

Thus, the solution is p = 2 and q = 3.

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