EasyMathematicsHigh School (9–10)GeneralAlgebra › Pairs of Linear EquationsAlgebra › Linear Equations in Two VariablesConceptualBoard Exam
Use the ratios, without solving, to find how many solutions each pair has…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Use the ratios, without solving, to find how many solutions each pair has.
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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. Pair (a). , , . All equal: the same line, infinitely many solutions.
Step 2. Pair (b). , , . The last differs: parallel lines, no solution.
Step 3. Pair (c). and differ: the lines cross, one solution. It is .
Answer: (a) infinitely many, (b) none, (c) exactly one.
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