Study Notes
In algebra, equations and inequalities are fundamental concepts used to find unknown values. Linear Equations — equations that form a straight line when graphed. Example: 7z - (3z - 4) = 12 simplifies to z = 2. Simultaneous Equations — a set of equations with multiple unknowns that are solved together. Example: Solving 3x + y = 19 and x + y = 9 gives x = 5 and y = 4. Inequalities — mathematical statements that compare two expressions using inequality symbols. Example: x > 5 means “x is more than 5.”
Exam Tips
Key Definitions to Remember
- Linear equations are equations that graph as straight lines.
- Simultaneous equations involve solving two or more equations together.
- Inequalities use symbols like >, <, ≥, and ≤ to compare values.
Common Confusions
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
- Mixing up the symbols for inequalities.
Typical Exam Questions
- Solve the equation 4a + 12 = -0.4 - a? Answer: a = -2.48
- Solve the simultaneous equations 2x + 3y = 5 and 5x - 2y = -16? Answer: x = -2, y = 3
- Solve the inequality 4 - 2x < 2? Answer: x > 1
What Examiners Usually Test
- Ability to simplify and solve linear equations.
- Solving simultaneous equations accurately.
- Correctly solving and representing inequalities on a number line.