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Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables

1. Solve:

Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables
Hint: Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables  ...(1)
Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables    ...(2)

Subtracting (1) from (2), Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables = an – bm or Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables
Thus, Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables
Ans.Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables

2. Solve : 141x + 103y = 217;   103x + 141y = 27
Ans. x = 3,  y = –2

3. Solve : 55x + 52y = 217;   52x + 55y = 217
Ans. x = 3,   y = 1

4. Solve :Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables
Ans. x = 4,   y = 3

5. Solve : Class 9 Maths Chapter 4 HOTS Questions - Linear Equations in Two Variables
Ans. x = 2;  y = 1

6. Solve : x + y = 18; y + z = 12;    z + x = 16
Ans. x = 11,  y = 7,  z = 5

The document Class 9 Maths Chapter 4 HOTS Questions - 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 HOTS Questions - Linear Equations in Two Variables

1. How do you solve a linear equation in two variables?
Ans. To solve a linear equation in two variables, you can use either the substitution method or the elimination method. In the substitution method, you solve one equation for one variable and substitute it into the other equation. In the elimination method, you add or subtract the equations to eliminate one variable and solve for the other.
2. 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. Each equation represents a line, and the solution to the system of equations is the point where the lines intersect. If the lines are parallel, there is no solution. If the lines overlap, there are infinitely many solutions.
3. How can you determine the number of solutions for a system of linear equations in two variables?
Ans. The number of solutions for a system of linear equations in two variables can be determined by analyzing the slopes and intercepts of the lines represented by the equations. If the slopes are different, the lines intersect at a single point, indicating a unique solution. If the slopes are the same and the intercepts are different, the lines are parallel with no solution. If the slopes and intercepts are the same, the lines overlap, indicating infinitely many solutions.
4. What is the importance of solving linear equations in two variables?
Ans. Solving linear equations in two variables is important as it allows us to find the intersection point of two lines, which has applications in various fields such as science, engineering, and economics. It helps in analyzing relationships between two variables and making predictions or decisions based on the obtained solutions. Additionally, it forms the foundation for more advanced concepts in algebra and mathematics.
5. Can a linear equation in two variables have more than one solution?
Ans. Yes, a linear equation in two variables can have more than one solution. If the two lines represented by the equations overlap, they have infinitely many points in common, indicating infinitely many solutions. This occurs when the equations are dependent on each other, meaning one equation is a multiple of the other. In such cases, any point on the overlapping line is a solution to the system of equations.
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