📐 Crack the Code of Equations! 🎉

Equations sit at the heart of almost every O-Level Maths question. From rearranging physics formulas to finding where two lines cross, **mastering equations unlocks huge marks** across the paper. In this post, we’ll tackle linear equations, simultaneous equations, and changing the subject—three skills that must be second-nature before exam day.

Core Concepts to Remember

A linear equation has the form $ax + b = 0$ and its graph is a straight line.
Simultaneous linear equations are two (or more) lines; their solution is the intersection point $(x, y)$ .
When you **change the subject** of a formula, treat the subject like the unknown you want alone on one side.

Worked Example: Solving Simultaneous Equations

Problem: Solve the simultaneous equations

\begin{cases}3x + 2y = 16\\2x - y = 1\end{cases}

Step 1: Multiply the second equation by $2$ so that $y$ will eliminate:
$4x - 2y = 2$
Step 2: Add this to the first equation:
$(3x + 2y) + (4x - 2y) = 16 + 2 \Rightarrow 7x = 18$
Step 3: Solve for $x$ :
$x = \frac{18}{7}$
Step 4: Substitute $x$ into $2x - y = 1$ :
$2\left(\frac{18}{7}\right) - y = 1 \Rightarrow y = \frac{29}{7}$
Solution: $(x, y) = \left(\frac{18}{7},\;\frac{29}{7}\right)$

Quick-Fire Practice Tips

Revise by mixing question types—solve one linear equation, then one simultaneous pair, then rearrange a formula like

v^2 = u^2 + 2as

to make

s

the subject. **Consistency beats cramming**. Keep practising until each step feels automatic, and the marks will follow!