Why is algebra efficient?

Answer 1

Consider it first as a set of instructions to perform 1 or more arithmetical operations on any related values:

V = IR means multiply I by R to find V whatever the values for I and R.

(This is Ohms' Law if the letters stand for Voltage, Current and Resistance in a simple electrical circuit!)

Consider next that you can alter the order and signs by definite rules:

If V = IR then R = V/I and I = V/R.

So we can abbreviate the operations, rather like a knitting-pattern or Chess notation - AND we can manipulate the original equation to suit the particular task.

So at once, even for a simple, practical use like that, we have an efficient, elegant way to express what we need to do to perform the task.