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

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

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?

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

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.