Question

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

Answer 1

Answer:

p = $\frac{35}{13}$ and q = $\frac{6}{13}$

Step-by-step 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 = $\frac{6}{13}$

(d)  Now substitute the value of q = $\frac{6}{13}$ into equation (i) as follows;

     2p - 3($\frac{6}{13}$) = 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 = $\frac{35}{13}$

Therefore, p = $\frac{35}{13}$ and q = $\frac{6}{13}$