Summary
Simultaneous equations involve solving two equations with two different unknowns to find the value of each term. There are two methods to solve simultaneous equations: 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 — solve one equation for one variable and substitute into the other equation. Example: Solve x + y = 9 for y, then substitute into 3x + y = 19.
- Elimination Method — multiply equations to make coefficients of one variable equal, then add or subtract equations to eliminate that variable. Example: Multiply 2x - y = 7 by 2 to eliminate y when added to 3x + 2y = 7.
Exam Tips
Key Definitions to Remember
- Simultaneous Equations: Two equations with two unknowns.
- Substitution Method: Solving one equation for a variable and substituting it into another.
- Elimination Method: Making coefficients equal to eliminate a variable.
Common Confusions
- Forgetting to substitute back to find the second variable.
- Incorrectly multiplying equations in the elimination method.
Typical Exam Questions
- How do you solve 3x + y = 19 and x + y = 9 using substitution? Solve x + y = 9 for y, substitute into 3x + y = 19.
- How do you solve 2x - y = 7 and 3x + 2y = 7 using elimination? Multiply 2x - y = 7 by 2, add to 3x + 2y = 7 to eliminate y.
- What is the cost of a pen and eraser if 2 pens and 1 eraser cost Rs.35 and 3 pens and 4 erasers cost Rs.65? Use simultaneous equations to solve for x and y.
What Examiners Usually Test
- Ability to correctly apply substitution and elimination methods.
- Understanding of how to manipulate equations to solve for unknowns.