Use elimination on 3x + 6y = 12 and x + 2y = 7…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Use elimination on and . What do you find, and what does it tell you about the two lines?
Need a reminder? The key ideaShow
Substitution: write one letter in terms of the other and put it into the second equation. Elimination: make the coefficients of one letter match, then add or subtract the equations. Always put the answer back into both equations. If both letters vanish, means infinitely many solutions and a false statement means none.
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 terms in . Multiply the second equation by : .
Step 2. Subtract it from the first equation. , which gives .
Step 3. Read the result. No values of and make equal , so the pair has no solution.
Step 4. The lines. Both lines have slope , but they cut the -axis at different points. They are parallel and never meet.
Answer: elimination ends in the false statement , so the lines are parallel and the pair has no solution.
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