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

(a) Concepts questions

(b) Calculation problems

(c) Multiple choice questions

(d) Long answer questions

(e) Fill in the blank's

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

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)

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.

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

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

Answer (b)

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

Answer (d)

Any point on the y-axis is of the form

(a) (x, 0)

(b) (x, y)

(c) (0, y)

(d) ( y, y)

Answer (C)

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.

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.

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

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.

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

Draw the graph of y = x + 2

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)

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.

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

Solve for y:

$ \frac {3y+2}{7} + \frac {4 (y+1)}{5}= \frac {2}{3} (2y+1)$

The angles of a triangle are 5x, 3 (2x - 5) and 9x -5 Find x and also name the triangle.

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

Determine the point on graph of equation 2x + 5y = 20 whose x - co-ordinate is 5/2 times its ordinate.

If (2a,a-1) is a solution of 2x + 3y - 9 = 0, find a

If (2a,a - 1) is the solution ,then putting x=2a and y=a-1

$2(2a) + 3(a-1) -9=0$

$4a + 3a -3 -9=0$

$a= 12/7$

Draw the graph of linear equation x = 3y

We can draw the graph by joining for points (0,0) and (3,1)

Draw the graph of linear equation 2x -9 = 0

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

Draw the graph of linear equation x = y

We can draw the graph by joining for points (0,0) and (1,1)

Draw the graphs of linear equation y = x and y = -x on the same Cartesian plane, what do you observe?

Here is the graph

We can observe that both the graph are symmetrical on both the x-axis and y-axis

Find three different solutions of the equation 4x + 3y = 12 from its graph?

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.

Draw the graph of the line x - 2y = 3. From the graph, find the co-ordinate of the point when

x = 5

y = -2

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

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