# Class 10 – Pair of Linear Equations in Two Variables – Important Questions

Pair of Linear Equations in Two Variables – Important Questions

1. Solve the following pair of equations:
3x + 4y = 10
2x – 2y = 2
2. Draw the graph of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0, using this graph, find the values of x and y satisfying both equations.
3. A motor boat whose speed in still water is 9 km/h, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.
4. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
5. Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
6. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
7. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
8. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
9. Solve the following pair of linear equations 5x + 3y = 35 and 2x + 4y = 28 by cross multiplication method.
10. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.