Urgent: maths questions!?

Question

1) 

3p+9q=51 
7p+9q=83 


2) 11s+9t=67 
4s+9t=53

Answer 1

1)

3p + 9q = 51                     -------------------(1)

7p + 9q = 83                    -------------------(2)

Subtract equation(1)  from equation(2)

(2) - (1) ⇒  ( 7p + 9q ) - ( 3p + 9q ) = 83 - 51

7p + 9q - 3p - 9q  = 32     ⇒    4p = 32      ⇒     p = 32 / 4

p = 8

 

(1)  ⇒  3p + 9q = 51

Substitute : p = 8.

3(8) + 9q = 51    ⇒   24 + 9q = 51    ⇒    9q = 27      ⇒    q = 27/9

q = 3

Solution : p = 8 , q = 3.

Answer 2

2)

11s + 9t = 67                      -------------------(1)

4s + 9t = 53                        -------------------(2)

Subtract equation(2)  from equation(1)

(1) - (2) ⇒  ( 11s + 9t ) - ( 4s + 9t ) = 67 - 53

11s + 9t - 4s - 9t = 14    ⇒   7s = 14    ⇒    s = 14/7

s = 2

 

(2)  ⇒  4s + 9t = 53

Substitute : s = 2.

4(2) + 9t = 53    ⇒    8 + 9t = 53    ⇒    9t = 53 - 8

9t = 45     ⇒     t = 45/9

t = 5

Solution : s = 2 , t = 5.