Question

Solve the following pair of simultaneous equations.

3x − 2y = 9, `x/2 - y/6 = 5/6`

Answer 1

Given equations:

3x − 2y = 9     ...(1)

`x/2 - y/6 = 5/6`    ...(2)

Here, multiplying equation (2) by 6:

`6(x/2 - y/6) = 6(5/6)`

`(6x)/2 - (6y)/6 = 5`

3x − y = 5    ...(3)

Now, subtracting equation (3) from equation (1):

(3x − 2y) − (3x − y) = 9 − 5

3x − 2y − 3x + y = 4

3x − 3x − 2y + y = 4

− 2y + y = 4

−y = 4

y = −4 + 1

∴ y = −3

Let’s substitute y = −3 into equation (1):

3x − 2(−3) = 9

3x − (−6) = 9

3x + 6 = 9

3x = 9 − 6

3x = 3

x = `3/3`

∴ x = 1