If 3p - q = 6 and 2p + 3q = 4, find q

To find the value of q, we need to solve the given system of equations:

3p - q = 6 ...(1)

2p + 3q = 4 ...(2)

One way to solve this system is to use the method of elimination, where we eliminate one of the variables by adding or subtracting the equations.

Multiplying equation (1) by 3, we get:

9p - 3q = 18 ...(3)

Now, we can eliminate q by adding equations (2) and (3):

2p + 3q = 4

9p - 3q = 18

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11p = 22

Dividing both sides by 11, we get:

p = 2

Substituting this value of p in equation (1), we get:

3(2) - q = 6

Simplifying this, we get:

6 - q = 6

Subtracting 6 from both sides, we get:

-q = 0

Dividing both sides by -1, we get:

q = 0

Therefore, q = 0 is the solution of the given system of equations.

In summary, to find the value of q, we used the method of elimination by multiplying equation (1) by 3 and adding it to equation (2) to eliminate q. This resulted in finding the value of p as 2. Substituting this value of p in equation (1), we found the value of q as 0.