Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Short Answer Type Questions: Linear Equations in Two Variables

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables

Question 1. Is (3, 2) a solution of x + y = 6?
Solution: (3, 2) means x = 3 and y = 2
∴ Substituting x = 3 and y = 2 in x + y = 6,
we have 3 + 2 = 6
⇒ 5 = 6 which is not correct Since
L.H.S. ≠ R.H.S.
∴ (3, 2) is not a solution of x + y = 6.


Question 2. Is Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables a solution of 2x + 3y = 12?
Solution: The given equation is 2x + 3y = 12  ...(1)

Here Solution = Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables

⇒ x = 2 and y = (8/3)
Substituting x = 2 and y =(8/3)  in (1), we get

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
⇒ 4 + 8 = 12
⇒ 12 = 12
∵ L.H.S. = R.H.S

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables is a solution of 2x + 3y = 12.


Question 3. Express Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variablesin the form of ax + by + c = 0 and write the value of a, b and c. 
Solution: We have Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables    ...(1)

Comparing (1) with ax + by + c = 0, we have
a = –2, b = (3/2) and c = –4.

Question 4. Express 2x = 5 in the form ax + by + c = 0 and find the value of a, b and c.
Solution: 2x = 5 can be written as 2x – 5 = 0
⇒ 2x + (0)y – 5 = 0
⇒ 2x + (0)y + (–5) = 0                                ...(1)
Comparing (1) with ax + by + c = 0, we get
a = 2,  b = 0 and  c = –5.


Question 5. Write two solutions of 3x + y = 8.
Solution: We have 3x + y = 8
For x = 0, we have 3(0) + y = 8
⇒ 0 x y= 8 ⇒ y = 8

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables  .e. (0, 8) is a solution.
For x = 1, we have 3(1) + y = 8
⇒ 3 + y = 8
⇒ y = 8 – 3 = 5 

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables    i.e. (1, 5) is another solution.


Question 6. If x = –1 and y = 2 is a solution of kx + 3y = 7, find the value k.
Solution: We have kx + 3y = 7                          ...(1)
∴ Putting x = –1 and y = 2 in (1), we get
k(–1) + 3(2) = 7
⇒ –k + 6 = 7
⇒ –k = 7 – 6 = 1
⇒ k= –1
Thus, the required value of k = –1.

Question 7. Show that x = 2 and y = 1 satisfy the linear equation 2x + 3y = 7.
Solution: We have 2x + 3y = 7                       ...(1)
Since, x = 2 and y = 1 satisfy the equation (1).
∴ Substituting x = 2 and y = 1 in (1), we get
L.H.S. = 2(2) + 3(1) = 4 + 3 = 7
= R.H.S.
Since, L.H.S. = R.H.S.
∴ x = 2 and y = 1 satisfy the given equation.

Question 8. Write four solutions of 2x + 3y = 8.
Solution: We have 2x + 3y = 8   ...(1)
Let us assume x = 0.
∴ Substituting x = 0 in (1), we get
2(0) + 3y = 8
⇒ 0 + 3y = 8
⇒ y= (8/3)

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables is a solution of (1)

Again assume y = 0.
∴ From (1), we have
2x + 3(0) = 8
⇒ 2x = 8
⇒   x= (8/2)  = 4

∴ (4, 0) is a solution of (1).
Again assume x = 1.
∴ From (1), we have
2(1) + 3y = 8
⇒ 3y = 8 – 2 = 6
⇒ y = (6/3) = 2
∴ (1, 2) is a solution of (1).
Again assume x = 2.
∴ From (1), we have
2(2) + 3y = 8
⇒ 4 + 3y = 8
⇒ 3y = 8 – 4 = 4
⇒ y = (4/3)

Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables is a solution of (1).

∴ The required four solutions are:Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables,  (4, 0), (1, 2) andClass 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables

The document Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables

1. What are linear equations in two variables?
Ans. Linear equations in two variables are algebraic equations that involve two variables, usually represented as x and y, and have a degree of 1. These equations can be written in the form ax + by = c, where a, b, and c are constants.
2. How do you solve a linear equation in two variables?
Ans. To solve a linear equation in two variables, we need to find the values of x and y that satisfy the equation. This can be done by either substitution method or elimination method. In the substitution method, we solve one equation for one variable and substitute it into the other equation. In the elimination method, we add or subtract the equations to eliminate one variable and then solve for the other.
3. What is the graphical representation of a linear equation in two variables?
Ans. The graphical representation of a linear equation in two variables is a straight line on a coordinate plane. Each point on the line represents a solution to the equation. If two lines intersect at a point, it means that the coordinates of that point satisfy both equations simultaneously.
4. Can a linear equation in two variables have infinitely many solutions?
Ans. Yes, a linear equation in two variables can have infinitely many solutions. This occurs when the two equations are equivalent or represent the same line. In such cases, every point on the line is a solution to the equation.
5. How can linear equations in two variables be used in real-life situations?
Ans. Linear equations in two variables have numerous applications in real-life situations. They can be used to solve problems related to cost and revenue, distance and time, speed and time, and many other scenarios where two variables are related. For example, they can help calculate the number of items that need to be sold to break even or determine the optimal combination of ingredients in a recipe.
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