Systems of Equations, Glossary

Knowing the vocabulary of Systems of Equations precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• System of Linear Equations in Three Variables, A system of linear equations in three variables consists of equations such as $x+y+z=6$ that must all hold together. A unique solution is a triple $(x,y,z)$ satisfying every equation. We usually solve it by elimination or substitution to reduce it step by step to a single variable. →
• Simultaneous Equations, Simultaneous equations are two or more equations solved together to find values that satisfy all of them at once. In this chapter one equation is linear and one is non-linear, such as a line meeting a curve. Substitution is the usual method, and there may be two solution pairs. →
• Substitution Method, The substitution method solves simultaneous equations by making one variable the subject of the linear equation, then replacing it in the non-linear equation. This leaves a single equation in one unknown, often a quadratic, which we solve before finding the matching value of the other variable. →
• Elimination Method, The elimination method removes one variable from a system by adding or subtracting suitable multiples of the equations, so their coefficients cancel. Repeating this reduces a three-variable system to two, then to one. It is efficient when coefficients line up neatly for cancellation. →
• Non-Linear Equation, A non-linear equation contains a term whose variable is not simply to the first power, for example $x^{2}$, $xy$, or $\frac{1}{x}$. Its graph is a curve rather than a straight line. In this chapter it is paired with a linear equation and solved simultaneously by substitution. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Systems of Equations chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Systems of Equations terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Systems of Equations questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.