# Class 9 – Linear Equations In Two variables – Important Questions

Linear Equations In Two variables – Important Questions

1. On the graph paper draw the straight line 3x – 2y = 4 and x + y – 3 = 0. Also, find their point of intersection on the graph.
2. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
3. Find the value of k, if (1, -1) is a solution of the equation 3x – ky = 8. Also, find the coordinate of another point lying on its graph.
4. The taxi fare in a city is as follows: For the first kilometre, the fare is ₹8 and for subsequent distances it is ₹5 per kilometre. Taking the distance covered as x and total fare as ₹y. Write a linear equation in two variable and draw its graph.
5. Give the geometric representation of 2x + 1 = x – 3 as an equation
(i) in one variable.
(ii) in two variables.
6. If (p, 2p + 1) is a solution of the linear equation 4x + 2y = 28. Find the value of p.
7. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
1. x – y/5 – 10 = 0
2. -2x + 3y = 6
3. y – 2 = 0
8. Show that the points A (1, 2), B ( – 1, – 16) and C (0, – 7) lie on the graph of the linear equation y = 9x – 7.
9. Draw the graph of the linear equation 3x + 4y = 6. At what points, the graph cuts X and Y-axis?
10. Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.
11. Mrs. Agarwal lost her purse containing 50 rupee and 100 Rupee notes amount to Rs 1500 in a shop. Next day shopkeeper found the purse during dusting. He immediately went to Mrs. Agarwal’s house and returned the purse and rupees Mrs. Agarwal appreciates the shopkeeper for his act.
Represent this situation as an equation and draw the graph. What value do you learn from the shopkeeper’s act?
12. How many linear equations in x and y can have a solution as (x = 2, y = -3)?