MediumMathematicsHigh School (9–10)GeneralAlgebra › Pairs of Linear EquationsAlgebra › Linear Equations in Two VariablesConceptual
Two different straight lines can meet at one point, but never at two points.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two different straight lines can meet at one point, but never at two points. Why? What does this tell you about the number of solutions of a pair of linear equations?
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. Two points fix a line. Only one straight line passes through two given points.
Step 2. The argument. If two lines shared two points, both would be the one line through those points. So they would not be different lines.
Step 3. For a pair. A pair of linear equations has one solution, none, or infinitely many. It can never have exactly two.
Answer: two shared points would make the lines the same line, so a pair never has exactly two solutions.
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