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Simultaneous Equations Assessment Prep

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Simultaneous Equations Assessment Prep

Mathematical equations and graphs illustration

📚 Part A: Method Selection & Basic Problems

WALT: Identify appropriate methods for solving simultaneous equations and apply them accurately.

1. Which method would be most efficient for solving this system? Circle your choice:

2x + 3y = 7
x = 4 - y

Substitution

Elimination

Graphical

2. Solve using substitution:

x + 2y = 8
x = 3y - 2

Solution: x = _______, y = _______

3. Solve using elimination:

3x + 2y = 12
2x - 2y = 8

Solution: x = _______, y = _______

4. A café sells coffee for $4 and muffins for $3. If 5 coffees and 3 muffins cost $29, and 2 coffees and 4 muffins cost $20, set up simultaneous equations to find the actual prices.

Let c = cost of coffee, m = cost of muffin

Equation 1: _________________

Equation 2: _________________

✏️ Part B: Complex Systems & Problem Solving

5. Solve this system involving fractions:

x/2 + y/3 = 5
2x - 3y = 6

Solution: x = _______, y = _______

6. Extension: Solve this nonlinear system:

x² + y² = 25
x + y = 7

Solutions: (_____, _____) and (_____, _____)

7. The sum of two numbers is 15 and their difference is 3. Find both numbers by setting up and solving simultaneous equations.

The two numbers are _______ and _______

8. A rectangle has a perimeter of 24 metres and its length is 2 metres more than twice its width. Find the dimensions.

Width = _______ metres, Length = _______ metres

🎯 Part C: Self-Assessment Checklist

Success Criteria - Tick when confident:

I can choose the most efficient method (substitution, elimination, or graphical)

I can solve linear simultaneous equations using substitution

I can solve linear simultaneous equations using elimination

I can set up simultaneous equations from word problems

I can solve systems involving fractions or decimals

I can interpret solutions in real-world contexts

I can solve simple nonlinear systems (extension)

9. Reflection: Which topic do you need to revise most before the assessment?
10. Study Goal: What will you focus on in your next study session?

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