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INTERNATIONAL INDIAN SCHOOL, RIYADH AC. YEAR - 2010 - 2011 CLASS : IX SUBJECT : MATHEMATICS LINEAR EQUATIONS IN TWO VARIABLES & QUADRILATERALS WORK SHEET Q. 1. Express the following informations in the form of linear equations : i. The cost of a table is 5 times the cost of a chair. ii. Cost of a pen is 1/6 the cost of a note book. iii. Two workers, Anil and Rahim together earn Rs. 580 a day. Q. 2. Find two solutions for each of the following equations : (a) x/2 + y/3 = 5 (b) 2x - 5y =10 (c) px + qy = 3 Q. 3. Express each of the following linear equation in the standard form & hence find the values of a, b & c in each case : (a) 2x + 3y = (b) 2x = -5y (c) 5x = 7 (d) 7y = 8 Q. 4. Check which of the following pair is the solutions of the equation 2 x – y = 4. (a) (b) (1,1) (c) (2,0) Q. 5. Draw the graph of each of the following linear equation in two variables : (a) 3 = 2x + y (b) y = 3x (c) x-y = 0 (d) x + y = 0 Q. 6. The fare of autorikshaw in a city is as follows : For the first kilometer, the are is Rs. 10 & for the subsequent distance it is Rs. 7 per km. Write a linear equation for this information & draw its graph . 7. ABCD is a trapezium such that CD||AB, if E is the midpoint of AD and EF||CD||AB. Prove that: a) F is the midpoint of BC b) EF= ½ (AB + CD) 8. Prove that the quadrilateral formed by joining the midpoints of sides of square is square. 9. If a diagonal of a parallelogram bisect one of the angles of the parallelogram. Prove that its diagonals are perpendicular bisector of each other. 10. In fig. find the value of BC if AE =BE=x, and AF=CF=y, EF=29 cm x y (a) 29x + 29y (b) 29 (c) 58 cm (d) 14.5 cm 11. P,Q, & R are respectively the mid points of the sides AB, BC & CA of ∆ABC. (a)If the perimeter of ∆ABC is 30 cm, find the perimeter of ∆PQR. (b) If the perimeter of ∆PQR is 20 cm, find the perimeter of ∆ABC. 12. If the point (2t, t+3) lies on the line representing the equation 2x -3y = ( -7) find the value of t. 13. If the point (2 , 3 ) lies on the line representing the equation 2x + ky = 10 find the value of k. 14. If the point (2 , m ) lies on the line representing the equation 2x + 3y = 10 find the value of m. 15. Draw the graph of each of the following linear equation in two variables and find the points where the line representing the equations meet (a) X-axis (b) Y-axis. 16. Express y in terms of x if 2(2x + 3y) - 5 (x-y ) = 10 17. Express x in terms of y if 5 (x - 3y) - 2 ( 2 x-y ) = 6 Q. 18. Solve the equation 2x + 1 = x – 2 & represent the solution on : (a) The number line b) Cartesian plane 19 . Draw the graph of the equation : 2(x-3) = 2y – (5+y) . From the graph find the value of : (a) x when y = 3 (b) y when x= 3 20. (a) Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. (b)Write down any three equations passing through the point (5, -2). PREPARED BY: ROY MATHEW