For each pair, say whether the lines cross, are parallel or coincide, and how many solutions the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
For each pair, say whether the lines cross, are parallel or coincide, and how many solutions the pair has.
- and
- and
- and
Need a reminder? The key ideaShow
Two lines cross (one solution, consistent), run parallel (no solution, inconsistent), or coincide (infinitely many solutions, consistent and dependent). Multiply one equation to match the left sides. Different right sides mean parallel lines, equal right sides mean the same line.
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. (a) The second equation is times the first, including the right side (). The lines coincide: infinitely many solutions.
Step 2. (b) The left sides are the same, but the right sides are and . One expression cannot equal both, so the lines are parallel: no solution.
Step 3. (c) No number turns into , so the lines cross: exactly one solution.
Answer: (a) coincide, infinitely many solutions; (b) parallel, none; (c) cross, one.
Discussion (0)
Log in to join the discussion.
Loading…