Question

Two simultaneous equations are given below, where p and q are constants.

3x-py = 4
4x - 3y + q = 0
The solution to these equations is x = 1, y = 2.
Find the value of p and q.

Answer 1

p = -1/2

q = 2

Explanation:

Equations are:
3x - py = 4 [1]

4x - 3y + q = 0 [2]

If x = 1 and y = 2, then substituting for these values in each equation will provide a solution for p and q

Plugging x = 1 in Equation [1]:
3(1) - p(2) = 4

→ 3 - 2p = 4

→ -2p = 4 - 3

-2p = 1

-2p/-2 = 1/-2

p = -1/2

For the second equation 4x - 3y + q = 0
x = 1, y = 2

→ 4(1) -3(2) + q = 0

→ 4 - 6 + q = 0

→ -2 + q =0

→ q = 2