#### Chapters

Chapter 2 - Exponents of Real Numbers

Chapter 3 - Rationalisation

Chapter 4 - Algebraic Identities

Chapter 5 - Factorisation of Algebraic Expressions

Chapter 6 - Factorisation of Polynomials

Chapter 7 - Introduction to Euclid’s Geometry

Chapter 8 - Lines and Angles

Chapter 9 - Triangle and its Angles

Chapter 10 - Congruent Triangles

Chapter 11 - Co-ordinate Geometry

Chapter 12 - Heron’s Formula

Chapter 13 - Linear Equations in Two Variables

Chapter 14 - Quadrilaterals

Chapter 15 - Areas of Parallelograms and Triangles

Chapter 16 - Circles

Chapter 17 - Constructions

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

Chapter 19 - Surface Areas and Volume of a Circular Cylinder

Chapter 20 - Surface Areas and Volume of A Right Circular Cone

Chapter 21 - Surface Areas and Volume of a Sphere

Chapter 22 - Tabular Representation of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data

Chapter 24 - Measures of Central Tendency

Chapter 25 - Probability

## Chapter 13 - Linear Equations in Two Variables

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Express the following linear equations in the form ax + by + c = 0 and indicate the values of

a, b and c in each case :

-2x + 3y = 12

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/2- 5 = 0`

Express the following linear equations in the form ax + by + c = 0 and indicate the values of

a, b and c in each case:

2x + 3y = 9.35

Express the following linear equations in the form ax + by + c = 0 and indicate the values of

a, b and c in each case:

3x = -7y

a, b and c in each case:

2x + 3 = 0

a, b and c in each case:

y – 5 = 0

a, b and c in each case:

4 = 3x

a, b and c in each case:

y = `x / 2`

Write the following as an equation in two variable :

2x = −3

Write the following as an equation in two variable :

y = 3

Write the following as an equation in two variable :

5x = `7/2`

Write the following as an equation in two variable :

y = `3/2 x`

The cost of ball pen is Rs. 5 less than half of the cost of fountain pen. Write this statement as

a linear equation in two variables.

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Write two solutions for the following equation :

3x + 4y = 7

Write two solutions of the following equation :

x = 6y

Write two solutions for the following equation :

x + 𝜋y = 4

Write two solutions for the following equation :

`2/3 x - y = 4`

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation :

5x – 2y = 10

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation :

−4x + 3y = 12

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation :

2𝑥 + 3𝑦 = 24

Check which of the following are solutions of the equation 2x – y = 6 and which are not :

(1) (3, 0) (2) (0, 6) (3) (2, −2) (4) (√3, 0 ) (5) `(1/2,-5)`

If x = −1, y = 2 is a solution of the equation 3x + 4y = k, find the value of k.

Find the value of 𝜆, if x = −𝜆 and y =`5/2`

is a solution of the equation x + 4y – 7 = 0.

If x = 2𝛼 + 1 and y = 𝛼 – 1 is a solution of the equation 2x−3y + 5 = 0, find the value of 𝛼.

If x = 1 and y = 6 is a solution of the equation 8x – ay + a2 = 0, find the value of a.

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Draw the graph of the following linear equations in two variables:- x + y = 4

Draw the graph of the following linear equations in two variables:- x – y = 2

Draw the graph of the following linear equation in two variable : –x + y = 6

Draw the graph of the following linear equation in two variable : y = 2x

Draw the graph of the following linear equation in two variable : 3x + 5y = 15

Draw the graph of the following linear equation in two variable : ` x / 2 - y/ 3 = 2`

Draw the graph of the following linear equation in two variable : `(x-2)/3 = y - 3`

Draw the graph of the following linear equations in two variable : 2𝑦 = −𝑥 + 1

Give the equations of two lines passing through (3, 12). How many more such lines are there,

and why?

A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent

kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation

representing the above information.

A lending library has a fixed charge for the first three days and an additional charge for each

day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs 𝑥

and per day charges are Rs y. Write the linear equation representing the above information.

A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s

digit are x and y respectively, write the linear equation representing the above statement.

The sum of a two digit number and the number obtained by reversing the order of its digits

is 121. If units and ten’s digit of the number are x and y respectively then write the linear

equation representing the above statement.

Plot the points (3, 5) and (− 1, 3) on a graph paper and verify that the straight line passing

through these points also passes through the point (1, 4).

From the choices given below, choose the equation whose graph is given in Fig. below.

(i) y = x (ii) x + y = 0 (iii) y = 2x (iv) 2 + 3y = 7x

[Hint: Clearly, (-1, 1) and (1, -1) satisfy the equation x + y = 0]

From the choices given below, choose the equation whose graph is given in fig. below.

(i) y = x + 2 (ii) y = x – 2 (iii) y = −x + 2 (iv) x + 2y = 6

[Hint: Clearly, (2, 0) and (−1, 3) satisfy the equation y = −x + 2]

If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of k.

Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the

point: (i) whose y-coordinates is 3. (ii) whose x-coordinate is −3.

Draw the graph of the equation given below. Also, find the coordinates of the point

where the graph cuts the coordinate axes : 6x − 3y = 12

Draw the graph of the equation given below. Also, find the coordinates of the point

where the graph cuts the coordinate axes : −x + 4y = 8

Draw the graph of the equation given below. Also, find the coordinates of the point

where the graph cuts the coordinate axes : 2x + y = 6

Draw the graph of the equation given below. Also, find the coordinate of the points

where the graph cuts the coordinate axes : 3x + 2y + 6 = 0

Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the

coordinate axes. Also, find the area of the shaded region.

Draw the graph of the equatio ` x / y + y /4 = 1` Also, find the area of the triangle formed by the

line and the co-ordinates axes.

Draw the graph of y = | x |.

Draw the graph of y = | x | + 2.

Draw the graphs of the following linear equations on the same graph paper: 2x + 3y = 12, x

– y = 1.

Find the coordinates of the vertices of the triangle formed by the two straight lines and the

y-axis. Also, find the area of the triangle.

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 path of a train A is given by the equation 3x + 4y − 12 = 0 and the path of another train

B is given by the equation 6x + 8y − 48 = 0. Represent this situation graphically.

Ravish tells his daughter Aarushi, “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 present ages

of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as

well as graphically.

Aarushi was driving a car with uniform speed of 60 km/h. Draw distance-time graph. From

the graph, find the distance travelled by Aarushi in

(1) ` 2 1/2` Hours (2) ` 1/2 ` Hour

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Give the geometric representation of the following equation

(a) on the number line (b) on the Cartesian plane : y + 3 = 0

Give the geometric representation of the following equation

(a) on the number line (b) on the Cartesian plane : y = 3

Give the geometric representation of the following equation

(a) on the number line (b) on the Cartesian plane : 2x + 9 = 0

Give the geometric representation of the following equation

(a) on the number line (b) on the Cartesian plane : 3x – 5 = 0

Give the geometrical representation of 2x + 13 = 0 as an equation in one variable .

Give the geometrical representation of 2x + 13 = 0 as an equation in two variables .

Solve the equation 3x + 2 = x − 8, and represent the solution on the number line .

Solve the equation 3x + 2 = x − 8, and represent the solution on the

Cartesian plane .

Write the equation of the line that is parallel to x-axis and passing through the point (0, 3) .

Write the equation of the line that is parallel to x-axis and passing through the point (0, -4) .

Write the equation of the line that is parallel to x-axis and passing through the point (2, -5) .

Write the equation of the line that is parallel to x-axis and passing through the point (3, 4) .

Write the equation of the line that is parallel to y-axis and passing through the point (4, 0) .

Write the equation of the line that is parallel to y-axis and passing through the point (−2, 0 ) .

Write the equation of the line that is parallel to y-axis and passing through the point (3, 5) .

Write the equation of the line that is parallel to y-axis and passing through the point (− 4, −3) .