Question

Solve the following simultaneous equations by the substitution method.

`(2x)/3 + y/4 = 3, x/3 - y/4 = 0`

Answer 1

Given simultaneous equations:

`(2x)/3 + y/4 = 3` and  `x/3 - y/4 = 0`

Step 1: Express one variable in terms of the other from the second equation

From `x/3 - y/4 = 0` we get

`x/3 = y/4`

⇒ `y = 4/3 x`

Step 2: Substitute `(y = 4/3 x)` into the first equation

First equation:

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

Substitute (y):

`(2x)/3 + 1/4 xx 4/3 x = 3`

Simplify:

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

Note `(4x)/(12) = x/3`, 

So, `(2x)/(3) + x/3 = 3`.

⇒ `(3x)/(3) = 3` 

⇒ x = 3

Step 3: Find (y) using `(y = 4/3 x)`

`y = 4/3 xx 3`

y = 4