A variable is just a name for a number we don’t know yet. An equation is what pins that number down. The question this lesson turns on: how many equations does it take to pin down how many unknowns — and what happens once that number gets large?

One Unknown 3 apples cost 6 riyals

Let be the price of one apple — the unknown we want to find. Three apples costing 6 riyals means three copies of that unknown add up to 6.

One unknown, one equation, one answer: each apple costs 2 riyals.

The Rule Match the count of equations to the count of unknowns

One unknown needs one equation. Two unknowns need two equations. Three need three — and the pattern keeps going: ten unknowns need ten equations. This counting rule is the whole lesson.

Two Unknowns 3 apples + 4 oranges = 18 riyals — one equation is not enough

Let

be the apple price and

the orange price:

. One equation, two unknowns — every point on this line is a valid pair.

All three pairs satisfy the same equation, so it cannot tell them apart. A second equation is needed to pick out just one.

Second Equation A friend’s purchase pins it down

A friend bought 5 apples and 1 orange from the same shop for 13 riyals:

. Two equations, two unknowns — now solvable.

Solve one equation for a variable, substitute it into the other, and only one point survives both lines at once: , .

Summary

One unknown needs one equation: .
A single equation in two unknowns has infinitely many solutions — a whole line of them.
Two unknowns need two equations: and together give , .
Scale this up to ten unknowns and hand substitution becomes unreliable — which is exactly why matrices exist: an organized, scalable method that works the same way for any number of equations.

The Concept of Equations