Friday, 18 November 2011

Tips On Using Substitution

Maths entails the usage of our brain juice in solving problems. It is a good platform for stretching our imagination and creativity by using simple concepts learned to handle seemingly complex maths questions.

Let's look at a "complex" simultaneous equations maths problem, and its way of solving (suggested).

Question:

$\dpi{120} \fn_cs \frac{1}{y}+\frac{1}{x}= \frac{81}{8}$  ---- (A)

$\dpi{120} \fn_cs \frac{1}{2y}+\frac{2}{x}= \frac{21}{4}$ --- (B)

Solve for y and x.

How do you go about it?

Look scary, right?

But like what I said, looks can be deceiving. Use the brain to go around the issue!

Tips: The structure of the simultaneous equations looks similar to the conventional type.
(Conventional type:-
Ax + By = nn
Cx + Dy = kk      )

So what we have to do can be to simply substitute $\dpi{120} \fn_cs \frac{1}{y}$ by m, and $\dpi{120} \fn_cs \frac{1}{x}$ by h (or any variable name).

What we thus convert to is:
$\dpi{120} \fn_cs m + h = \frac{81}{8}$  ---- (A)

$\dpi{120} \fn_cs \frac{m}{2} + 2h = \frac{21}{4}$ --- (B)

Will this simultaneous equations be more comfortable to solve?

Hence, a simple twist to the former mathematical questions can result in a totally familiar situations where we have solve many a times.

Thus, the technique and usefulness of substitution cannot be under-estimated.

It can be powerful at times to reveal a beautiful mathematical expression for user to resolve.

Maths Is Interesting!

Treasure our brain and our thinking.

:-)