Is the point (3, 2) a solution of the pair x + 2y = 7 and 3x - y = 5? …
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Is the point a solution of the pair and ? Work out the left side of each equation at the point, and say yes or no.
Need a reminder? The key ideaShow
The graph of a linear equation in two variables is a straight line, and every point on it is a solution. A solution of a pair is a point on both lines: it fits both equations. Put the numbers into both equations to check. For fares, write each fare as and make the two equal.
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. The first equation. . This matches the right side, .
Step 2. The second equation. . The right side is , so this does not match.
Step 3. Decide. The point fits the first equation only.
Answer: No. is on the first line but not on the second, so it is not a solution of the pair.
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