Question

3. If 2p + q = 11 and p + 2q = 13, then

p+q=
(A) 6
(B) 8
(C) 9
(D) 12
(E) 18

Answer 1

Answer:
(C) 9

Step by step:
11-2=9 and it’s asking for both p and q combined so no need to worry about that

Answer 2

The correct answer is ( B ) 8.

Explanation:

We will first solve the two simultaneous equations for the values of 'p' and 'q' respectively.

Equation No. 1 -

2p + q = 11

Equation No. 2 -

p + 2q = 13

We will make 'q' the subject in Equation No. 1 and substitute the expression for 'q' into Equation No. 2.

Equation No. 1 -

q = 11 - 2p

Equation No. 2 -

p + 2 ( 11 - 2p ) = 13

We will solve Equation No. 2 for the value of 'p'.

Equation No. 2 -

p + 22 - 4p = 13

p - 4p = 13 - 22

- 3p = - 9

p = - 9 ÷ - 3

p = 3

We will substitute the obtain value for 'p' from Equation No. 2 into Equation No. 1 to find the value of 'q'.

Equation No. 1 -

q = 11 - 2 ( 3 )

q = 5

We will substitute the obtained values for 'p' and 'q' from Equation No. 1 and Equation No. 2 into p + q.

= p + q

= 3 + 5

= 8

Therefore:

The correct answer is ( B ) 8.