Stage 9 - Q1 - 2 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q2 - 2 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q3 - 3 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q4 - 3 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q5 - 4 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q6 - 4 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q7 - 5 marks
12 tickets are sold: adult tickets cost USD 5 and child tickets USD 2. The total is USD 57. Find the numbers of each using elimination.
Hint
Make the child-ticket coefficients equal before subtracting.
Stage 9 - Q8 - 5 marks
Solve by elimination. Check both equations.
Hint
Opposite coefficients cancel by adding; equal coefficients cancel by subtracting.
Stage 9 - Q9 - 5 marks
The system has solution \(x=3\), \(y=2\). Find \(k\), then show elimination recovers the pair.
Hint
The constant must make the second original equation true.
Stage 9 - Q10 - 3 marks
Three adult tickets and two child tickets cost USD 26. Two adult tickets and three child tickets cost USD 24. Find each price using elimination and verify both totals.
Hint
Multipliers 3 and 2 make the child-ticket coefficients equal.