Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1: Give the geometric representations of the following equations

(a) on the number line 

(b) on the Cartesian plane:

(i) x = 2
 (ii) y + 3 = 0
 (iii) y = 3
 (iv) 2x + 9 = 0
 (v) 3x – 5 = 0

Ans :

(i) We are given, x = 2

The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to y axis passing througl-the point (2, 0) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(ii)  We are given, y + 3 = 0

We get, Y = -3

The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to x axis passing through the point A(0, —3) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(iii) we are given. y = 3

The representation of the solution on the number line. when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to x axis passing through the point (0, 3) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(iv) We are given, 2x +9 = 0

We get,  2x = -9 The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to y axis passing through the point ( -9/2,0) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(v) We are given, 3x —5 = 0

We get, 5 x = 3 The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to y axis passing througl-the point (5,0) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q 2 : Give the geometrical representation of 2x + 13 = 0 as an equation in

(i) one variable
 (ii) two variables

Ans:

We are given,

2x +13 = 0

We get,

2x = -13

x = -13/2

The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation of the solution on the Cartesian plane, it is a line parallel to y axis passing through the point (-13/2 , 0) is shown below.

Q3:. Solve the equation 3x + 2 = x – 8, and represent the solution on

(i) the number line
 (ii) the Cartesian plane.

Ans : We are given,

3x + 2 = x – 8

we get,

3x – x =  -8 – 2

2x = -10

x = -5

The representation of the solution on the number line, when given equation is treated as an equation in one variable.

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The representation Of the solution on the Cartesian plane, it is a line parallel to y axis passing through the point (-5, 0) is shown below

RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q 4:  Write the equation of the line that is parallel to x-axis and passing through the points

(i) (0,3)
 (ii) (0, – 4)
 (iii) (2,-5)
 (iv) (3,4)

Ans:

(i) We are given the co-ordinates of the Cartesian plane at (0,3).

For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to 3.

We get the equation as y = 3

(ii) We are given the co-ordinates of the Cartesian plane at (0,-4).

For the equation of the line parallel to x axis, we assume the equation as a one variable equation Independent of x containing y equal to -4.

We get the equation as y = -4

(iii) We are given the co-ordinates of the Cartesian plane at (2,-5).

For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to -5.

We get the equation as y = -5

(iv) We are given the co-ordinates of the Cartesian plane at (3,4).

For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to 4.

We get the equation as

y = 4

Q 5 : Write the equation of the line that is parallel to y-axis and passing through the Points

(i) (4,0)
 (ii) (-2,0)
 (iii) (3,5)
 (iv) (- 4, – 3)

Ans:

(i) We are given the coordinates of the Cartesian plane at (4,0)-

For the equation of the line parallel to y axis ,we assume the equation as a one variable equation independent of y containing x equal to 4

We get the equation as y = 3

(ii) We are given the coordinates of the Cartesian plane at (-2,0) –

For the equation of the line parallel to y axis, we assume the equation as a one variable equation independent of y containing x equal to -2

We get the equation as y = -4

(iii) We are given the coordinates of the Cartesian plane at (3,5)-

For the equation of the line parallel to y axis, we assume the equation as a one variable equation independent of y containing x equal to 3

We get the equation as y = -5

(iv) We are given the coordinates of the Cartesian plane at (-4,-3)-

For the equation of the line parallel to y axis, we assume the equation as a one variable equation independent of y containing x equal to -4

We get the equation as y = 4

The document RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on RD Sharma Solutions Ex-13.4, Linear Equation In Two Variables, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics

1. What are linear equations in two variables?
Ans. Linear equations in two variables are algebraic equations that involve two variables, usually represented by 'x' and 'y', and have a degree of one. These equations can be graphically represented as straight lines on a Cartesian plane.
2. How do you solve linear equations in two variables?
Ans. To solve linear equations in two variables, we use various methods such as the substitution method, elimination method, and cross-multiplication method. These methods involve manipulating the equations to eliminate one variable and find the values of the remaining variable.
3. How can linear equations in two variables be represented graphically?
Ans. Linear equations in two variables can be represented graphically by plotting points on a Cartesian plane and joining them to form a straight line. Each point on the line represents a solution to the equation, and the slope of the line determines the relationship between the variables.
4. What is the importance of linear equations in two variables in real-life applications?
Ans. Linear equations in two variables have numerous real-life applications, such as in economics, physics, and engineering. They are used to model and solve problems involving rates of change, cost and revenue analysis, optimization, and many other scenarios where two variables are interrelated.
5. Can linear equations in two variables have infinitely many solutions?
Ans. Yes, linear equations in two variables can have infinitely many solutions. This occurs when the two equations represent the same line or are parallel lines. In such cases, every point on the line(s) represents a solution to the equations.
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