Study Notes
Solving equations and inequalities involves finding the values of variables that satisfy given conditions. Linear equations have variables with an exponent of 1 and form a straight line when graphed. Inequalities use symbols like <, >, ≤, and ≥ to show relationships between expressions.
- Linear Equation — An equation where the highest degree of the variable is 1.
Example: 8 - 10x = 6 - Inequality — A mathematical statement that compares two expressions using inequality symbols.
Example: x > 5 means "x is more than 5" - Simultaneous Equations — Two or more equations with multiple unknowns that are solved together.
Example: 3x + y = 19 and x + y = 9 - Substitution Method — Solving one equation for one variable and substituting into another equation.
Example: Solve y = 9 - x and substitute into 3x + y = 19 - Elimination Method — Adding or subtracting equations to eliminate a variable.
Example: Solve 2x - y = 7 and 3x + 2y = 7 by elimination
Exam Tips
Key Definitions to Remember
- Linear Equation: An equation with the highest degree of 1
- Inequality: A statement comparing two expressions with inequality symbols
- Simultaneous Equations: Equations with multiple unknowns solved together
Common Confusions
- Mixing up inequality symbols like < and ≤
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number
Typical Exam Questions
- Solve 8 - 10x = 6? x = 0.2
- Solve 4 - 2x < 2? x > 1
- Solve the simultaneous equations 3x + y = 19 and x + y = 9? x = 5, y = 4
What Examiners Usually Test
- Ability to solve linear equations and inequalities
- Understanding of graphing inequalities on a number line
- Solving simultaneous equations using substitution and elimination methods