Solving Simultaneous Linear Equations Together
Year 10 Mathematics Building problem-solving skills through collaboration Differentiated learning for all ability levels
What Are Simultaneous Linear Equations?
Two or more linear equations with the same variables Must be solved together to find common solutions Solutions satisfy ALL equations simultaneously Real-world applications in business, science, and engineering
Quick Check: Identify the Variables
Look at these equation pairs: 2x + 3y = 12 x - y = 1 What variables do we need to find? What does a solution look like?
Method 1: Substitution
Solve one equation for one variable Substitute this expression into the other equation Solve for the remaining variable Substitute back to find the first variable
Practice: Substitution Method
Work in pairs to solve: Equation 1: y = 2x + 1 Equation 2: 3x + y = 11 Extension: Create your own system and solve
Method 2: Elimination
Multiply equations to create opposite coefficients Add or subtract equations to eliminate one variable Solve for the remaining variable Substitute back to find the other variable
Substitution vs Elimination
{"left":"Best when one equation is already solved for a variable\nUseful when coefficients are simple\nGood for equations with fractions","right":"Best when coefficients can be easily made opposite\nEfficient for integer coefficients\nSystematic approach for complex systems"}
Real-World Challenge
A school canteen sells pies for $4 and sandwiches for $6 Yesterday they sold 50 items and made $260 How many pies and sandwiches were sold? Set up and solve the simultaneous equations
Extension Challenge
Three-variable system: x + y + z = 6 2x - y + z = 3 x + 2y - z = 4 Advanced: Solve using matrix methods
Summary and Next Steps
Mastered substitution and elimination methods Applied skills to real-world problems Recognized when to use each method Ready for systems with special cases (no solution, infinite solutions)