The line 3x + 4y = 12 is drawn. A second line is 6x + 8y = c…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The line is drawn. A second line is . Find so that the two lines coincide. What happens if ?
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. Match the left sides. .
Step 2. Match the right sides. For the same line, .
Step 3. If . The left sides still match but , so the lines are parallel and the pair has no solution.
Answer: . With the lines are parallel.
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