Monday, 18 August 2008

Tips To Reduce Errors Doing Simultaneous Equations

Solving simultaneous equations involves many simple steps. The simple steps mostly include addition, subtraction and multiplication.

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.


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.


No comments: