Though the mathematical operations are simple, mistakes made while solving simultaneous equations are aplenty. The errors are mostly "slip-of-the-mind" human errors.

To review the

**elimination method**employed to solve simultaneous equations, please

**click here**.

How then are we to reduce these careless errors?

Here, I propose 2 tips.

__Tip one__**Make use of addition instead of subtraction to eliminate the selected unknown.**

Example:

**( to eliminate unknown "y")**

7x + 2y = 11 --- (A)

-5x + 2y = -1 --- (B)

In normal doing, we perform (A) - (B) equation subtraction. But what is the risk?

The result may end up as

*!*

**2x + 0 = 10**The

**correct answer**should be

**12x + 0 = 12**.

Why the error?

This is because our brain is use to addition more than subtraction. Therefore the "slip-of- the-mind" error happened.

Mentally doing 7x - (-5x) is harder to operate with.

Refer to

**this post**to understand why our brain likes addition.

So how?

Negate the equation (B) so that we can perform addition.

(-5x + 2y) times (-1) = -1 times (-1)

will become 5x - 2y = 1 ----(C)

Rewriting the question,

7x + 2y = 11 ----(A)

5x - 2y = 1 ----(C)

This becomes simpler!

We now need to

**ADD**the 2 equations. (Instead of the risky subtraction).

(A) + (C) : 12x + 0 = 12 <== This is the correct result that we want, risk-free!

**Message**: Negate the unknown variable of one equation and do ADDITION to remove it.

__Tip two__**Avoid making the number (coefficient) bigger through multiplication.**

Example:

9x + 2y = 13 --- ( K )

x - 4y = -7 --- ( L )

Here, we have the option to remove either the "x" or the "y".

Which to select depends on the proper selection of multiplication factor

*.*

**in order not to make the coefficient big**Case 1: Remove "x".

We need to multiply equation (L) by 9 to cause the first term (x) to be the same as that in equation (k), so as to eliminate the "x" unknown.

**What happened?**

Equation (L) became 9x -

**36**y = - 63 !

Look at the coefficient of "y" ===> It became a

**GIANT**!

Case 2: Remove unknown "y".

Multiply equation (k) by 2. This produces equation (k) as 18x + 4 y = 26.

This is still manageable. And less error will occur since

*big number is harder to handle*.

**Message**: Seek to multiply coefficient such that the resultant equation has smaller number.

I have seen many maths students fumbling with these simple operations, and making many unnecessary mistakes.

I do hope that these two little tips will aid you and any maths learners of simultaneous equations to reduce errors.

:-P

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