HardMathematicsHigh School (9–10)GeneralAlgebra › Pairs of Linear EquationsAlgebra › Linear Equations in Two VariablesNumericalBoard ExamSAT
For which value of k does the pair 3x + ky = 7 and 6x + 15y = 5 have no solution? …
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
- For which value of does the pair and have no solution?
- With that , which number should replace the so that the pair has infinitely many solutions?
Need a reminder? The key ideaShow
Two lines cross at one point (one solution), run parallel (no solution) or lie on top of each other (infinitely many solutions). Compare , and to tell which.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Equal first two ratios. , so .
Step 2. Check the third ratio. is not , so the lines are parallel and the pair has no solution.
Step 3. The same line. We need , so .
Answer: ; replacing by makes the two lines one.
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