A shop says that 2 pens and 3 notebooks cost ₹51…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A shop says that pens and notebooks cost ₹51. A second bill says that pens and notebooks cost ₹99. The bills do not agree. For what total price would the second bill agree with the first? Is the pair of bills consistent as written?
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. Compare. The second bill is exactly twice the first in the number of pens and notebooks.
Step 2. The price that agrees. Twice ₹51 is ₹102.
Step 3. The bills as written. ₹99 is not ₹102, so the two equations describe parallel lines. No prices fit both bills.
Answer: ₹102 would agree. As written, the pair is inconsistent.
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