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Simultaneous equations and parameter constraints
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Practise the method.
Simultaneous equations and parameter constraints
Optional extension. Simultaneous equations and parameter constraints
Example 1
Solve 5x+6y=5 and 5x−6y=3. Find x+y.
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Answer: 26
- Adding gives 52x=8
- x=20.
- Subtracting gives y=6.
- Their sum is 26.
Example 2
The equations 2x+5y=7 and px+25y=35 have infinitely many solutions. Find p.
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Answer: 10
- The second equation must be 5 times the first.
- Its x coefficient must therefore be 10.
Example 3
Solve 3x+2y=4 and 3x−2y=2. Find x+y.
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Answer: 11
- Adding gives 32x=6
- x=9.
- Subtracting gives y=2.
- Their sum is 11.
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