Study Notes
Simultaneous linear equations involve solving two equations with two different unknowns to find the value of each unknown. The two main methods to solve these equations are substitution and elimination.
- Simultaneous Equations — two equations with two unknowns that need to be solved together.
Example: 3x + y = 19 and x + y = 9. - Substitution Method — involves expressing one variable in terms of the other and substituting it into the second equation.
Example: Solve 3x + y = 19 and x + y = 9 by expressing y as 9 - x and substituting into the first equation. - Elimination Method — involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.
Example: Solve 2x - y = 7 and 3x + 2y = 7 by multiplying and adding equations to eliminate y.
Exam Tips
Key Definitions to Remember
- Simultaneous equations involve two equations with two unknowns.
- Substitution method involves expressing one variable in terms of another.
- Elimination method involves adding or subtracting equations to eliminate a variable.
Common Confusions
- Mixing up which variable to eliminate in the elimination method.
- Forgetting to substitute back to find the second variable after solving for the first.
Typical Exam Questions
- Solve 3x + y = 19 and x + y = 9 using substitution? Express y in terms of x, substitute into the first equation, solve for x, then find y.
- Solve 2x - y = 7 and 3x + 2y = 7 using elimination? Multiply equations to align coefficients, add or subtract to eliminate y, solve for x, then find y.
- A store sells 4 hard drives and 10 pen drives for 290. Find the cost of each? Set up equations for each scenario, use elimination or substitution to solve.
What Examiners Usually Test
- Ability to correctly apply substitution and elimination methods.
- Understanding of how to manipulate equations to facilitate solving.
- Accuracy in solving for both variables and checking solutions.