Question

Solve the following pair of simultaneous equations.

`(2x)/3 + (3y)/4 = 7`, 5x = 3y + 18

Answer 1

Given equations:

`(2x)/3 + (3y)/4 = 7`     ...(1)

5x = 3y + 18     ...(2)

Here, multiplying equation (1) by 12:

`12((2x)/3 + (3y)/4) = 12(7)`

`(24x)/3 + (36y)/4 = 84`

8x + 9y = 84     ...(3)

And, simplifying equation (2):

5x = 3y + 18

5x − 3y = 18     ...(4)

Also, multiplying equation (4) by 3:

3(5x − 3y) = 3(18)

15x − 9y = 54     ...(5)

Now, adding equation (3) and equation (5):

(8x + 9y) + (15x − 9y) = 84 + 54

8x + 9y + 15x − 9y = 138

8x + 15x + 9y − 9y = 138

23x = 138

`x = 138/23`

∴ x = 6

Let’s substitute x = 6 into equation (4):

5(6) − 3y = 18

30 − 3y = 18

−3y = 18 − 30

−3y = −18

`y = (-18)/-3`

∴ y = 4