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Simultaneous equations and parameter constraints
Free examples and worked answers. No account needed.
Practise the method.
Simultaneous equations and parameter constraints
Optional extension. Simultaneous equations and parameter constraints
Example 1
For which value of k does the system kx+4y=1 and 25x+20y=0 have no solution?
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Answer: 5
- The determinant is 20k−100.
- It is zero at k=5.
- At that value the left sides are proportional but the right sides are not.
Example 2
The equation x+5kx+21=6 has solution x=−9. Find k. (Exclude x=−5.)
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Answer: 5
- Substitute x=−9 and multiply by−4:−9k+21=−24.
- Solving gives k=5.
Example 3
For which value of k does the system kx+2y=1 and 25x+10y=0 have no solution?
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Answer: 5
- The determinant is 10k−50.
- It is zero at k=5.
- At that value the left sides are proportional but the right sides are not.
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