Q) Solve the following system of linear equations : 2p + 3q = 13 and 5p – 4q = – 2

Ans: Given equations are:

2p + 3q = 13 …… ………….. (i)

and 5p – 4q = – 2 …………… (ii)

To get the value of variables, we need to drop one variable.

Let’s multiply (i) by 4 and (ii) by 3 and add them up:

∴ 4 (2 p + 3 q) + 3 (5 p – 4 q) = 4 x 13 + 3 x (- 2)

∴ 8 p + 12 q + 15 p – 12 q = 52 – 6

∴ 23 p = 46

∴ p = = 2

Transferring value of p = 2 in equation (i), we get:

2 p + 3 q = 13

∴ 2 (2) + 3 q = 13

∴ 4 + 3 q = 13

∴ 3 q = 13 – 4 = 9

∴ q = = 3

Therefore, values of p and q are 2 and 3 respectively.

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