Context, sequence/table, graph and formula representations; Two-variable simultaneous equations; Graph/technology solution and non-unique systems
Example 1
Adult tickets cost $7, child tickets $2. A group buys 7 tickets for $34. Find the number of adult tickets.
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Answer: 4
- Let adults x and children y. Use x+y= ticket count and the revenue equation, then eliminate y.
Example 2
Solve x+y=8 and 2x−y=1. Find x.
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Answer: 3
- Add the equations to eliminate y, giving 3x=3a.
Example 3
The equations y=2x+1 and 2y=4x+5 represent:
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Answer: Parallel distinct lines: no solution
- The second simplifies to y=2x+2.5; gradients agree but intercepts differ.