Linear Equations in Two Variables Class 9 Worksheet
Q.1: Express the following
linear equations in the form ax + by + c = 0 and indicate the values of a, b
and c in each case:
(i) x – y/5 – 10 = 0 (ii) y – 2 = 0
Q.2: Draw the graph of each
of the following linear equations in two variables:
(i) y = 3x (ii) 3 = 2x + y
Q.3: If the point (3, 4)
lies on the graph of the equation 3y = ax + 7, find the value of a.
Q.4: 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.
Q.5: Find m, if point (7, -
3) lies on the equation (y – 3/7) = m(x – 2/7).
Q.6: A fraction becomes 1/3, if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 2/5. Assuming the original fraction to be x/y, form a pair of linear equations in two variables for the problem.
Q.7: Draw the graph of the
linear equation y = mx + c for m = 1/2 and c = 3/2. Read from the graph, the
value of x, when y = 4.5.
Q.8: Draw the graph of the
linear equation 3x + 4y = 6. At what points, the graph cuts x and y-axis?
Q.9: If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is 2 units and 0 unit.
Q.10: The taxi fare in a
city is as follows: For the first kilometre, the fare is ₹ 8 and for the
subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total
fare as ₹ y, write a linear equation for this information, and draw its graph.
Q.11: Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.
Q.12: Give the geometric
representations of 2x + 9 = 0 as an equation:
a) in one variable b) in two variables
Q.13: Mohan tells his daughter Aarv, ‘Seven years ago, I was seven
times as old as you were then also, three years from now, I shall be three
times as old as you will be.’ If the present ages of Aarv and Mohan are x and y
years respectively, represent this situation algebraically as well as graphically.
Q.14: A and B are friends. A is elder to B by 5 years. B’s sister C is half the age of B while A’s father D is 8 years older than twice the age of B. If the present age of D is 48 years, find the present ages of A, B and C.
Q.15: The parking charge for vehicles in super Delhi Metro is ₹ 40 for first two hrs and ₹ 10 for subsequent hr. Assume total parking time to be x hrs. (where x ≥ 2) and total parking charge as y. Write the linear equation for above relation and draw graph. Find the parking charges for 5 hrs from graph.
Q.16.Thrice the cost of a kettle is equal to five times the cost of
an oven. Write a linear equation in two variables to represent this statement.
Q.17: Draw the graph of the equation y = mx + c for m = 3 and c = -1 (a straight line in Cartesian plane). Read from the graph the value of y when x = 2.
Q.18: If x is the number of hours a labourer is on work and y is his wages in rupees, then y = 4x + 3. Draw the work wages graph of this equation. From the graph, find the wages of a labourer who puts in 4 hours of work.
Q.19: Shivam is half of
his father’s age. Twenty years ago, the age of father was six times age of Shivam.
Find the present ages of Shivam and his father.
Q.20: Find the coordinates of the points where the line represented by the linear equation y = 2x – 4 intersects x-axis and y-axis.
ANSWERS
1. (i) 5x –
y – 50 = 0;
a = 5, b = -1, c = -50
(ii) 0.x + y – 2 = 0
a = 0, b = 1, c = -2
2. (i)
|
x |
1 |
2 |
-1 |
|
y |
3 |
6 |
-3 |
Plot the points (1, 3), (2, 6), (-1,
-3) on the graph paper to find the graph.
(ii)
|
x |
0 |
1 |
2 |
|
y |
3 |
1 |
-1 |
Plot the points (0, 3), (1, 1), (2, -1)
on the graph paper to find the graph.
3. a = 5/3
4. Do it yourself
5. m = -24/47
6. 3x – y = -4 ……. (1)
5x – 2y = -9 ……. (2)
7. x = 6
8. The graph cuts x-axis at (2, 0).
The graph cuts y-axis at (0, 1.5).
9. w = 5d; w = 10 units and 0 units
10. 5x – y = -3
11. 3x – y = 0
12. Do it yourself
13. 7x – y = 42 ….. (1)
3x – y = -6 ….. (2)
14. A: 25 years
B: 20 years
C: 10 years
15. y = 10x + 20; ₹ 70
16. 3k = 5o
17. y = 3x – 1; y = 5
18. y = 19
19. Shivam: 25 years
Father: 50 years
20. At x-axis: (2, 0)
At y-axis: (0, -4)
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