Pair of Linear Equations for Math Olympiad: Complete Guide

Why This Matters

Pair of linear equations is a topic where knowing multiple solving methods gives you a significant edge. Substitution, elimination, cross-multiplication, and graphical methods — each has situations where it shines.

For Class 10 students, Olympiad papers test not just your solving ability, but your judgment in choosing the most efficient method for each problem.

Best Strategy

Practice Questions

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Question 1

A boat goes 30 km upstream and 44 km downstream in 10 hours. It goes 40 km upstream and 55 km downstream in 13 hours. Find the speed of the boat and the stream.

Solution: Let boat speed = $x$, stream speed = $y$.
$\frac{30}{x-y} + \frac{44}{x+y} = 10$ and $\frac{40}{x-y} + \frac{55}{x+y} = 13$
Let $\frac{1}{x-y} = a$, $\frac{1}{x+y} = b$.
$30a + 44b = 10$ and $40a + 55b = 13$
Solving: $a = \frac{1}{5}$, $b = \frac{1}{11}$
$x - y = 5$, $x + y = 11$. So $x = 8$ km/h, $y = 3$ km/h.

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