Find solution for given equations 5p + 7q = 45 and 7p - q = 9.

 

Given equations: 

5p + 7q = 45 ---- (1)

7p - q = 9 ---- (2)

Since 'q' has opposite sign. Therefore, we will make coefficient of 'q' same.

L.C.M (7, 1) = 7

Multiply eqn (2) by 7, we get: 

49p - 7q = 63 ---- (3)

Adding eqn(1) & eqn(3) we get:

$\Rightarrow$5p + 7q + 49p - 7q = 45 + 63

$\Rightarrow$ 54p = 108

$\Rightarrow$ p = 2

Now, put value of p = 2 in eqn(2), we get:

$\Rightarrow$7p - q = 9 

$\Rightarrow$7(2) - q = 9 

$\Rightarrow$14 - q = 9

$\Rightarrow$q = 5