Question

Solve the following system of linear equations:

2p + 3q = 13 and 5p − 4q = −2

Answer 1

2p + 3q = 13         ...(i) 

5p − 4q = −2        ...(ii)

On multiplying eq. (i) by 4 and eq. (ii) by 3

(2p + 3q = 13) × 4

(5p − 4q = −2) × 3

On adding both equations

8p + 12q = 52

15p − 12q = −6
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            23p = 46
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               p = `46/23`

p = 2

Put p = 2 in eq. (i)

2(2) + 3q = 13

4 + 3q = 13

3q = 9

⇒ q = `9/3`

q = 3

⇒ p = 2 and q = 3