Question

Solve the following pair of simultaneous equations.

`x/2 + y/3 = 9 and x/5 - y/4 = -1`

Answer 1

Given equations:

`x/2 + y/3 = 9`    ...(1)

`x/5 - y/4 = -1`    ...(2)

Here, multiplying equation (1) by 6:

`6(x/2 + y/3) = 6(9)`

`(6x)/2 + (6y)/3 = 54`

3x + 2y = 54    ...(3)

And, multiplying equation (2) by 20:

`20(x/5 - y/4) = 20(-1)`

`(20x)/5 - (20y)/4 = -20`

4x − 5y = −20    ...(4)

Also, multiplying equation (3) by 5:

5(3x) + 5(2y) = 5(54)

15x + 10y = 270    ...(5)

Same for equation (4), multiply by 2:

2(4x) − 2(5y) = 2(−20)

8x − 10y = −40    ...(6)

Now, adding equation (5) and equation (6):

(15x + 10y) + (8x − 10y) = 270 − 40 

15x + 10y + 8x − 10y = 230

15x + 8x + 10y − 10y = 230

23x = 230

x = `230/23`

∴ x = 10

Let’s substitute x = 10 into equation (3):

3(10) + 2y = 54

30 + 2y = 54

2y = 54 − 30

2y = 24

y = `24/2`

∴ y = 12