Question

Solve the following pair of simultaneous equations.

9x − 5y = 52, 4x − 3y = 27

Answer 1

Given equations:

9x − 5y = 52    ...(1)

4x − 3y = 27    ...(2)

Here, multiplying equation (1) by 3:

3(9x − 5y) = 3(52)

27x − 15y = 156    ...(3)

And, multiplying equation (2) by 5:

5(4x − 3y) = 5(27)

20x − 15y = 135    ...(4)

Now, subtracting equation (4) from equation (3):

(27x − 15y) − (20x − 15y) = 156 − 135

27x − 15y − 20x + 15y = 21

27x − 20x − 15y + 15y = 21

7x = 21

x = `21/7`

∴ x = 3

Let’s substitute x = 3 into equation (2):

4(3) − 3y = 27 

12 − 3y = 27

−3y = 27 − 12

−3y = 15

y = `15/-3`

∴ y = −5