NCERT Solutions: Linear Equations in Two Variables (Exercise 4.1)

# Linear Equations in Two Variables (Exercise 4.1) NCERT Solutions - Mathematics (Maths) Class 9

Q1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y)
Ans: Let the cost of a notebook be = ₹ x
Let the cost of a pen be = ₹ y
According to the question,
The cost of a notebook is twice the cost of a pen.
i.e., cost of a notebook = 2×cost of a pen
x = 2 × y
x = 2y
x - 2y = 0
x - 2y = 0 is the linear equation in two variables to represent the statement, ‘The cost of a notebook is twice the cost of a pen.’

Q2. 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=
Ans: Consider 2x + 3y=     Equation (1)
⇒ 2x + 3y - = 0
Comparing this equation with the standard form of the linear equation in two variables, ax + by + c = 0 we have,
a = 2
b = 3
c = -

(ii) x – (y/5) – 10 = 0
Ans: The equation x –(y/5)-10 = 0 can be written as,
(1)x+(-1/5)y +(–10) = 0
Now comparing x+(-1/5)y+(–10) = 0 with ax+by+c = 0
We get,
a = 1
b = -(1/5)
c = -10

(iii) –2x + 3y = 6
Ans: –2x+3y = 6
Re-arranging the equation, we get,
–2x+3y–6 = 0
The equation –2x+3y–6 = 0 can be written as,
(–2)x+(3)y+(– 6) = 0
Now, comparing (–2)x+(3)y+(–6) = 0 with ax+by+c = 0
We get, a = –2
b = 3
c =-6

(iv) x = 3y
Ans: x = 3y
Re-arranging the equation, we get,
x-3y = 0
The equation x-3y=0 can be written as,
(1)x+(-3)y+(0)c = 0
Now comparing 1x+(-3)y+(0)c = 0 with ax+by+c = 0
We get a = 1
b = -3
c = 0

(v) 2x = –5y
Ans: 2x = –5y
Re-arranging the equation, we get,
2x+5y = 0
The equation 2x+5y = 0 can be written as,
2x+5y+0 = 0
Now, comparing (2)x+(5)y+0= 0 with ax+by+c = 0
We get a = 2
b = 5
c = 0

(vi) 3x + 2 = 0
Ans: 3x+2 = 0
The equation 3x+2 = 0 can be written as,
3x+0y+2 = 0
Now comparing 3x+0+2= 0 with ax+by+c = 0
We get a = 3
b = 0
c = 2

(vii) y–2 = 0
Ans: y–2 = 0
The equation y–2 = 0 can be written as,
(0)x+(1)y+(–2) = 0
Now comparing (0)x+(1)y+(–2) = 0with ax+by+c = 0
We get a = 0
b = 1
c = –2

(viii) 5 = 2x
Ans: 5 = 2x
Re-arranging the equation, we get,
2x = 5
i.e., 2x–5 = 0
The equation 2x–5 = 0 can be written as,
2x+0y–5 = 0
Now comparing 2x+0y–5 = 0 with ax+by+c = 0
We get a = 2
b = 0
c = -5

The document Linear Equations in Two Variables (Exercise 4.1) NCERT Solutions | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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## FAQs on Linear Equations in Two Variables (Exercise 4.1) NCERT Solutions - Mathematics (Maths) Class 9

 1. What are linear equations in two variables?
Ans. Linear equations in two variables are equations that can be written in the form of Ax + By = C, where A, B, and C are constants and x and y are variables. These equations represent straight lines on a coordinate plane.
 2. How do you solve a system of linear equations in two variables?
Ans. To solve a system of linear equations in two variables, you can use different methods such as substitution, elimination, or graphing. In substitution, you solve one equation for one variable and substitute it into the other equation. In elimination, you manipulate the equations so that when added or subtracted, one variable is eliminated. Graphing involves plotting the equations on a coordinate plane and finding the point of intersection.
 3. What is the importance of linear equations in two variables?
Ans. Linear equations in two variables have various applications in real-life situations. They can be used to solve problems related to cost and revenue, distance and speed, and many other situations that involve two variables. They provide a mathematical representation of relationships between variables and help in making predictions and solving practical problems.
 4. Can linear equations in two variables have more than one solution?
Ans. Yes, linear equations in two variables can have one solution, no solution, or infinitely many solutions. If the equations represent two distinct lines that intersect at a single point, they have one solution. If the equations represent parallel lines, there is no solution. However, if the equations represent the same line, there are infinitely many solutions as any point on the line satisfies both equations.
 5. What is the graphical representation of linear equations in two variables?
Ans. The graphical representation of linear equations in two variables is a straight line on a coordinate plane. Each equation represents a line, and the point of intersection between the lines represents the solution of the system of equations. If the lines are parallel, there is no solution, and if the lines coincide, there are infinitely many solutions. By analyzing the slope and y-intercept of the lines, you can determine their characteristics and relationship.

## Mathematics (Maths) Class 9

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## Mathematics (Maths) Class 9

62 videos|426 docs|102 tests

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