Equations — NSW Year 9 Core Maths
Linear equations with the pronumeral on one or both sides, brackets and fractions, formulas, worded problems and simple quadratics. Six subtopics and 120 practice questions with worked solutions, aligned to MA5-EQU-C-01.
Equations in NSW Year 9
An equation says two expressions are equal, and solving it means finding the value that makes this true. In Year 9 Core students solve linear equations of a few steps, including ones with the pronumeral on both sides, brackets and a fraction, such as \(\frac{2x + 1}{3} = \frac{x + 4}{2}\). They then use equations to work with formulas, solve worded problems, and meet simple quadratic equations such as \(4x^2 - 9 = 27\).
The six subtopics below cover variables on one side, variables on both sides, equations with brackets, using formulae, equation problems and quadratic equations. Equations is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Number and Algebra strand. The linear work is Stage 5 Core content under NESA outcome MA5‑EQU‑C‑01, and the quadratic equations come from MA5‑EQU‑P‑01, which goes beyond the Core outcomes. Solving equations is used straight away in Earning Money and Straight Line, and leads to simultaneous and quadratic equations in Year 10.
Subtopics
Equations: common questions
How do you solve an equation with the pronumeral on both sides?
Gather the pronumeral terms on one side first, usually by subtracting the smaller one, then solve as usual. For \(5x + 2 = 3x + 10\), subtract \(3x\) to get \(2x + 2 = 10\), so \(2x = 8\) and \(x = 4\).
How do you solve an equation with brackets?
Expand the brackets, collect like terms, then solve. For \(3(x - 2) = x + 4\), expanding gives \(3x - 6 = x + 4\), so \(2x = 10\) and \(x = 5\).
How do you turn a word problem into an equation?
Choose a pronumeral for the unknown and say what it stands for, write each part of the description in terms of it, then form the equation. If a number doubled and increased by \(7\) gives \(19\), then \(2x + 7 = 19\), so \(x = 6\).
Why does a quadratic equation have two solutions?
Both a positive and a negative number give the same square. Since \(7^2 = 49\) and \((-7)^2 = 49\), the equation \(x^2 = 49\) has the solutions \(x = 7\) and \(x = -7\), written \(x = \pm 7\).
Which NESA outcomes cover equations in Year 9?
Linear equations of up to three steps, including brackets, one algebraic fraction, formulas and word problems, are Stage 5 Core content under MA5‑EQU‑C‑01. Simple quadratic equations come from MA5‑EQU‑P‑01, which goes beyond the Core outcomes.