linear equations in two variables class 9 worksheet
Given below are the Linear equations in two variables class 9 worksheet with solutions
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(d) Long answer questions
(e) Fill in the blank's
Question 1
Draw the graph of each of the equations given below. Also, find the co-ordinates of the point where the graph cuts the co-ordinates axis:
(a) 6x - 4y = 12
(b) 4y -x= 8 Solution
To draw the graph, we need at least two solutions of the equation
We can get two points by putting x=0 and y=0. And then draw the graph. Corrdinates will be given by (x,0) and (0,y)
a.
Coordinates are (2,0) and (0,-4)
b.
Coordinates are (-8,0) and (0,2)
Question 2
The taxi fare in a delhi is as follows: For the first kilometer, the fare is Rs16 and for the subsequent distance it is Rs 10/km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph. Solution
Total fare = Fare of first kilometer + 10 × subsequent distance travelled
$y= 16 + 10 (x-1)$
$y=16 + 10x- 10$
$y=6+10x$
We can draw the graph by putting points x=0 and x=1
Question 3
If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form
(a) y - x = 0
(b) x + y = 0
(c) -2x + y = 0
(d) -x + 2y = 0 Solution
Answer (b)
Question 4
Which of the below statement is true
(a) A linear equation x + 3y = 5 has a unique solution
(b) The graph of the equation y = x + 1 passes through the origin
(c) The line parallel to the y-axis at a distance 4 units to the left of y-axis is given by the equation y = - 4
(d) None of the above Solution
Answer (d)
Question 5
Any point on the y-axis is of the form
(a) (x, 0)
(b) (x, y)
(c) (0, y)
(d) ( y, y) Solution
Answer (C)
Question 6
Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the point:
Whose y- coordinate is 3
Whose x- coordinate is -3.
Question 7
Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the co- ordinate axis. Also find the area of shaded region. Solution
The graph of the equation 2x + y = 6 can be drawn by choosing points x=0 i.e y=6 and y=0 i.e x=3
Shading the region bounded by the graph and the co- ordinate axis
This is a right angle triangle with base =3 and height =6
So area = $\frac {1}{2} \times 6 \times 3 = 9 $units
Question 8
Draw the graph of the equation $ \frac {x}{2} + \frac {y}{3} =1$. Also find the area of triangle formed by the line and the co-ordinates axis. Solution
The graph of the Linear equation $ \frac {x}{2} + \frac {y}{3} =1$ can be drawn by choosing points x=0 i.e y=3 and y=0 i.e x=2
Now the triangle formed by the line and co-ordinates axis is given as below
This is a right angle with base as 2 units and height ad 3 units.
So ,Area = $\frac {1}{2} \times 2 \times 3= 3$ units
Question 9
Draw the graph of y = x + 2 Solution
We can get two points by putting x=0 and y=0. And then draw the graph. Corrdinates will be given by (x,0) and (0,y)
Question 10
Draw the graphs of the linear equations 4x - 3y + 4 = 0 and 4x + 3y - 20 = 0. Find the area bounded by these lines and x = axis. Solution
The graph of 4x - 3y + 4 = 0 by putting y=0 i.e x= -1 and x=2 i.e y =4
Similarly the graph 4x + 3y - 20 = 0 by putting y=0 i.e x=5 and x=2 i.e y=4
Now we can see that area bounded by these lines and x = axis is a triangle with base = 6 unit and height =4 units.
So area = $\frac {1}{2} \times 6 \times 4 = 12 $units
Question 12
The angles of a triangle are 5x, 3 (2x - 5) and 9x -5 Find x and also name the triangle. Solution
We know that sum of the angles in the triangle is equal to 180
Therefore,
$5x + 3(2x - 5) + 9x -5=180$
$20 x -20 =180$
$x= 10$
Therefore angles are
50°, 45° , 85°
The name of the triangle is scalene triangle
Question 13
Determine the point on graph of equation 2x + 5y = 20 whose x - co-ordinate is 5/2 times its ordinate.
Question 14
If (2a,a-1) is a solution of 2x + 3y - 9 = 0, find a Solution
If (2a,a - 1) is the solution ,then putting x=2a and y=a-1
$2(2a) + 3(a-1) -9=0$
$4a + 3a -3 -9=0$
$a= 12/7$
Question 15
Draw the graph of linear equation x = 3y Solution
We can draw the graph by joining for points (0,0) and (3,1)
Question 16
Draw the graph of linear equation 2x -9 = 0 Solution
This can be treated as equation in two variable as
$ 2x + 0 \times y -9=0$
Drawing the graph by putting y=0 and y=2
Question 17
Draw the graph of linear equation x = y Solution
We can draw the graph by joining for points (0,0) and (1,1)
Question 18
Draw the graphs of linear equation y = x and y = -x on the same Cartesian plane, what do you observe? Solution
Here is the graph
We can observe that both the graph are symmetrical on both the x-axis and y-axis
Question 19 Find three different solutions of the equation 4x + 3y = 12 from its graph?
Question 20 Draw the graph of the equation x + 2y = 9. Find the vertices of the triangle formed by the line and the co-ordinate axis. Find two more points other than the intercepts on the axis.
Question 21 Draw the graph of the line x - 2y = 3. From the graph, find the co-ordinate of the point when
x = 5
y = -2
Summary
This Linear equations in two variables class 9 worksheet with solutions is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail. You can download this test as pdf also as below
