Parallel and identical lines
Parallel and identical lines
Secondary 2
Consider the simultaneous equations \(x-2y=4\) and \(3x-6y=k\), where \(k\) is a constant.
- Find the value of \(k\) for which the equations have infinitely many solutions, and write down two of the solutions.
- State the number of solutions when \(k=10\). Explain your answer.
- Explain, using the gradients of the two lines, why no value of \(k\) gives exactly one solution.
Solution:
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Answer:(a) \(k=12\); for example \((4,0)\) and \((0,-2)\)
(b) no solution (parallel lines)
(c) both gradients are \(\dfrac{1}{2}\)
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