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

Important Questions**Linear Equations In Two variables – Important Questions**

**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.****Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k**.**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.****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.****Give the geometric representation of 2x + 1 = x – 3 as an equation****(i) in one variable.****(ii) in two variables.****If (p, 2p + 1)****is a solution of the**linear equation 4x + 2y = 28. Find the value of p.**Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:****x – y/5 – 10 = 0****-2x + 3y = 6****y – 2 = 0**

**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**.**Draw the graph of the linear equation 3x + 4y = 6. At what points, the graph cuts X and Y-axis?****Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.****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?**How many linear equations in x and y can have a solution as (x = 2, y = -3)?**

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