Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.

A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Complete the activity to find the value of x.
3x + 2y = 11 …(i) and 2x + 3y = 4 …(ii)
Solution:
Multiply equation (i) by _______ and equation (ii) by _______.
`square` × (3x + 2y = 11)    ∴ 9x + 6y = 33 …(iii)
`square` × (2x + 3y = 4)      ∴ 4x + 6y = 8   …(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`

Solve 0.4x + 0.3y = 1.7; 0.7 x − 0.2y = 0.8

If  `|( 4,5), (m , 3)|` = 22, then find the value of m.