Question

Solve the simultaneous equation,
2p - 3q = 4
3p + 2q = 9

Answer 1

p =
`(35)/(13)` and q =
`(6)/(13)`

Explanation:

Given equations:

2p - 3q = 4 -----------(i)

3p + 2q = 9 ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4] x 3

[3p + 2q = 9] x 2

6p - 9q = 12 -------------(iii)

6p + 4q = 18 -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

[6p - 9q = 12]

- [6p + 4q = 18]

-13q = -6 -----------------(v)

(c) Next, make q subject of the formula in equation (v)

q =
`(6)/(13)`

(d) Now substitute the value of q =
`(6)/(13)` into equation (i) as follows;

2p - 3(
`(6)/(13)`) = 4

(e) Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p =
`(35)/(13)`

Therefore, p =
`(35)/(13)` and q =
`(6)/(13)`