Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-13.1, Linear Equation In Two Variables, Class 9, Maths

RD Sharma Solutions Ex-13.1, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

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) -2x + 3y = 12
(ii) x – y/2 – 5 = 0
(iii) 2x + 3y = 9.35 
(iv) 3x = -7y
(v) 2x + 3 = 0
(vi) y – 5 = 0
(vii) 4 = 3x
(viii) y = x/2 ;

A 1 :

(i) We are given

– 2x + 3y = 12

– 2x  + 3y – 12 = 0

Comparing the given equation with ax+ by+ c = O

We get, a = – 2; b = 3; c = -12

(ii) We are given

x – y/2 – 5= 0

Comparing the given equation with ax + by + c = 0 ,

We get, a = 1; b = -1/2, c = -5

(iii) We are given

2x + 3y = 9.35

2x + 3y – 9.35 =0

Comparing the given equation with ax + by + c = 0

We get, a = 2 ; b = 3 ; c = -9.35

(iv) We are given

3x = -7y

3x + 7y = 0

Comparing the given equation with ax+ by + c = 0,

We get, a = 3 ; b = 7 ; c = 0

(v) We are given

2x + 3 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 2 ; b = 0 ; c = 3

(vi) We are given

Y – 5 = 0

Comparing the given equation with ax + by+ c = 0,

We get, a = 0; b = 1; c = -5

(vii) We are given

4 = 3x

3x-4 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 3; b = 0; c = -4

(viii) We are given

Y = x/2

Taking L.C.M ⇒ x — 2y = 0

Comparing the given equation with ax + by + c = 0 ,

We get, a = 1; b = -2; c = 0


Q 2: Write each of the following as an equation in two variables:

(i) 2x = -3
(ii) y=3 
(iii) 5x = 7/ 2
(iv) y = 3/2x

A 2:

(i) We are given,

2x = -3

Now, in two variable forms the given equation will be

2x + 0y + 3 = 0

(ii) We are given,

y = 3

Now, in two variable forms the given equation will be

0 x + y – 3 = 0

(iii) We are given,

5x = -7/2

Now, in two variable forms the given equation will be

5x + Oy +7/2 = 0

10x + Oy – 7  = 0

(iv) We are given,

RD Sharma Solutions Ex-13.1, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics  (Taking L.C.M on both sides)

Now, in two variable forms the given equation will be

3x – 2y + 0 = 0

Q 3 :  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.

A 3:

Let the cost of fountain pen be y and cost of ball pen be x.

According to the given equation, we have

RD Sharma Solutions Ex-13.1, Linear Equation In Two Variables, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

⇒ 2x = y – 10

⇒ 2x –y + 10 = 0

Here y is the cost of one fountain pen and x is that of one ball pen.

The document RD Sharma Solutions Ex-13.1, 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-13.1, Linear Equation In Two Variables, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics

1. What is a linear equation in two variables?
Ans. A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are the variables. It represents a straight line on a graph and has infinitely many solutions.
2. How can we solve a linear equation in two variables?
Ans. To solve a linear equation in two variables, we can use various methods such as substitution method, elimination method, and graphical method. In the substitution method, we solve one equation for one variable and substitute it into the other equation. In the elimination method, we eliminate one variable by adding or subtracting the equations. In the graphical method, we plot the equations on a graph and find their point of intersection.
3. Can a linear equation in two variables have more than one solution?
Ans. No, a linear equation in two variables can have either one solution, no solution, or infinitely many solutions. If the lines represented by the equations are parallel, there will be no solution. If the lines intersect at a single point, there will be one solution. If the lines coincide, there will be infinitely many solutions.
4. How do we represent the solution of a linear equation in two variables graphically?
Ans. The solution of a linear equation in two variables can be represented graphically by plotting the equations on a graph and finding their point of intersection. The coordinates of the point of intersection represent the solution of the equation. If the lines are parallel, there will be no point of intersection, indicating no solution.
5. Can a linear equation in two variables have different forms?
Ans. Yes, a linear equation in two variables can have different forms depending on the given information. The standard form of a linear equation is ax + by = c, where a, b, and c are constants. However, it can also be written in slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept. Both forms are equivalent and can be used interchangeably.
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