Question 1: Solve for x and y: 3x + 2y = 16 and 5x + 2y = 22 using matching coefficients.

Answer: x=2, y=5

Question 2: Construct the equations: A cyclist travels 60 km at a speed of 15 km/h and another takes a longer route totaling 100 km, with speeds matching the first cyclist’s speed. Write the simultaneous equations assuming both travel for the same time.

Answer: 15t=60 and 15t=100

Question 3: A map shows two routes from town A to town B. Route 1 is 120 km long and takes 3 hours. Route 2 is 150 km long and takes 4 hours. Assuming the same average speed for both routes, find the speed using matching coefficients.

Answer: Speed = 40 km/h

Question 4: A hiker plans two routes. Route 1 covers 80 km in 8 hours, and Route 2 covers 100 km in 10 hours. Set up equations to find the hiking speeds matching the times, then solve.

Answer: Speed1=10 km/h, Speed2=10 km/h

Question 5: In a city, two buses leave different stations heading towards each other. Bus A travels at 50 km/h, and Bus B at 60 km/h. They start 210 km apart. Write the equations for their meeting point and solve for the time when they meet.

Answer: t=2 hours

Question 6: A delivery truck makes two trips. On the first trip, it covers 180 km in 6 hours. On the second, it covers 220 km in 7 hours. Assuming constant speeds, set up matching coefficient equations to find the truck’s speed on each trip and solve.

Answer: Speed1=30 km/h, Speed2=31.43 km/h

Question 7: Two friends start from different cities and travel towards each other. Friend X travels at 80 km/h, and Friend Y at 70 km/h. They start 560 km apart. Write equations assuming they meet after t hours, then find t.

Answer: t=4 hours

Question 8: A train departs from station A travelling at 90 km/h and another from station B travelling at 100 km/h towards each other. The stations are 420 km apart. Write and solve the equations to find the time until they meet.

Answer: t=2 hours

Question 9: A boat crosses a river downstream and upstream. The downstream trip takes 2 hours, and the upstream trip takes 3 hours. Set up equations assuming the river current matches the boat’s speed, and find the boat’s speed relative to the water.

Answer: Boat speed=6 km/h, River current=2 km/h

Question 10: Error Analysis: A student sets up the equations 4x + 3y = 20 and 2x + 3y = 10 to find matching coefficients but gets an inconsistency. Identify the mistake and correct the equations.

Answer: Mistake is subtracting the equations incorrectly; correct equations: 4x + 3y = 20 and 4x + 3y = 20 for matching coefficients.