Question

Find the value of Q in the following system so that the solution to the system is

(3, 2).

4x - 5y = 2
6x + 7y = Q

A). 34 B). 32
C). 28 D). 30

Answer 1

The value of Q is B. 32.

Explanation:

Let's solve the system equation and let's find the value of Q.

4x - 5y = 2

6x + 7y = Q

1st equation

4x - 5y = 2

4x = 2 + 5y

x = 2/4 + 5y/4 (Dividing by 4 at both sides)

x = 1/2 + 5y/4

2nd equation

6x + 7y = Q

6 (1/2 + 5y/4) + 7y = Q

6/2 + 30y/4 + 7y = Q

3 + 30y/4 + 7y = Q

12 + 30y + 28y = 4Q (Multiplying by 4 at both sides)

58y = 4Q - 12

58y = 4 * 32 - 12 (Q = 32)

58y = 128 - 12

58y = 116

y = 2

Let's find the value of x

4x - 5y = 2

4x - 5 (2) = 2 (Replacing y)

4x - 10 = 2

4x = 2 + 10 (Like terms)

4x = 12

x = 3 (Dividing by 3 at both sides)