Simultaneous Equations | Re-write equations

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Simple simultaneous equation problem comes as 2 straight forward mathematical expressions.

Example 1:

3x + y = 4
x + 2y = 3

But some may come in odd expressions (since life is always the case, which makes learning maths more exciting!)

Example 2:

(12 - x)(1 + y) = 15
(8 - x) (1 + y) = -15

Here you will notice that the unknowns are biased towards one side.

Approach 1:
Multiply the 2 factors to get something like example 1.
Using elimination method, remove one of the unknown.
Solve for the only one unknown left.
Using the result found, compute the other unknown.

Approach 2:  (The focus of this post)
Re-write the expression to make it look simpler.

The example 2 can be re-written into below simpler form:
(12 - x) = 15 / (1 + y)  ===>  (A)
(8 - x) = -15 / (1 + y)   ===>  (B)

Equation (B) can then be seen to be the negative of equation (A).

With the re-writing, we will be visually aided to see another form, a simpler one, of the simultaneous equations.

Moving forward with the solution...

12 - x = -(8 - x) = -8 + x
12 + 8 = 2x
x = 20 / 2 = 10     (ANSWER)
Putting x = 10 back into either equation (A) or (B),

We will get (12 - 10) (1 + y) = 15,  if we select equation (A)
1 + y = 15 / 2 = 7.5
y = 7.5 - 1 = 6.5 (ANSWER)

The solution is not the issue in this post.

The key message here is the technique of "re-writing" the equations to reveal the simplicity of the question.

Maths is not that difficult if you look and think to make it easy.

Cheers!
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