Score Higher With Class 9 Linear Equations In Two Variables Exercise 4.2 Solutions
Class 9 Maths Chapter 4 exercise 4.2 Solutions focuses on solving linear equations in two variables. This essential part of algebra helps students understand how to handle equations with two unknowns. The important aspect here is to learn how to graph these equations and find solutions that satisfy both equations simultaneously.
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The key focus should be understanding the graphical method of solving equations, which involves plotting lines on a graph. The NCERT of Ex 4.2 class 9 also helps in visualising the solutions, making it easier to comprehend how equations interact. By mastering these concepts, students can tackle more complex problems with confidence.
You can download the FREE PDF for NCERT Solutions for Class 9 Maths from Vedantu and boost your preparations for Exams.
FAQs on NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations In Two Variables
1. How can you check if a point (x, y) is a solution to a linear equation?
Substitute the x and y values from the point into the equation. If the Left Hand Side (LHS) equals the Right Hand Side (RHS), the point is a solution. For 2x + y = 7, check (3,1): 2(3)+1 = 7. Since 7 = 7, it is a correct solution.
2. What is the method for downloading the Exercise 4.2 Class 9 PDF Solutions?
Navigate to the Vedantu NCERT Solutions page for Class 9 Maths Chapter 4. Find the link labelled "Download Free PDF" for Exercise 4.2. Click the link to save the solutions file to your device for offline access, making it easy to practise anytime.
3. How do you write a linear equation from a word problem?
Identify the two unknown quantities and assign them variables, like x and y. Translate the relationship described in the problem into a mathematical equation in the standard form Ax + By + C = 0. Always define what your variables represent before finalising the equation.
4. How can you find the value of a constant like 'k' in an equation if a solution is given?
Substitute the given x and y values of the solution directly into the equation. This creates a simple equation with 'k' as the only unknown. Solve this new equation to find the value of k. For example, if x=2, y=1 is a solution for 2x+3y=k, then k=2(2)+3(1)=7.
5. What is an effective way to use NCERT Solutions for revision before a test?
Use the solutions to quickly review the correct steps for important questions from Class 9 Maths Chapter 4 Exercise 4.2. Focus on problems you found difficult. Cover the solution, try solving it yourself first, and then verify your method and final answer.
6. How do you find four different solutions for a linear equation in two variables?
Instruction: Find multiple solutions for a linear equation like 2x + y = 7 by choosing simple integer values for one variable and then solving for the other.
Why it matters: A linear equation in two variables has infinitely many solutions. This method helps you find specific coordinate points, which is essential for plotting the equation's graph.
Steps:
- Rewrite the equation to isolate one variable. For example, convert 2x + y = 7 to y = 7 - 2x.
- Choose a simple value for x, like x = 0. Substitute it into the rewritten equation to find the corresponding y-value.
- Repeat this process with other easy-to-calculate values for x, such as 1, 2, and -1.
- Write each resulting (x, y) pair as a coordinate. These are your four solutions.
Check: To verify any solution, substitute both x and y values back into the original equation. The Left Hand Side must equal the Right Hand Side.
Isolate one variable, substitute simple values for the other, and solve to find corresponding pairs.
7. How can you use the step-by-step Class 9 Maths Chapter 4 Exercise 4.2 solutions to self-correct homework?
Instruction: Use the detailed solutions to check your work by comparing your entire method, not just the final answer.
Why it matters: This approach helps you find the exact point where you made a mistake, whether in calculation, formula application, or understanding. Simply checking the final answer doesn't reveal the source of an error.
Steps:
- First, attempt all the exercise problems from your NCERT textbook on your own.
- Open the solutions for Class 9 Maths Linear Equations in Two Variables Exercise 4.2.
- For each question, compare your solution step-by-step against the provided explanation.
- If your answer is incorrect, pinpoint the specific step where your method differs and correct it.
Tip: Don't just copy the correct answer. Make a note of the type of error you made (e.g., a sign mistake, wrong transposition) to avoid repeating it.
Solve problems first, then use the solutions to compare your steps and identify specific errors.
8. How can you tell if a linear equation in two variables has one, many, or no solutions?
Instruction: Recognise that any single linear equation in two variables of the form Ax + By + C = 0 (where A and B are not both zero) has infinitely many solutions.
Why it matters: This is a fundamental concept in Class 9 Maths Chapter 4. Unlike a linear equation in one variable, which has a unique solution, an equation with two variables represents a straight line on a graph. Every point on that line is a valid solution.
Steps:
- Confirm the equation is linear and contains two distinct variables (e.g., x and y).
- Understand that for any value you choose for x, you can always calculate a corresponding value for y.
- Since you can pick an infinite number of values for x, you can find an infinite number of matching y values.
Check: A single linear equation in two variables will never have "no solution" or just a "unique solution." For any question of this type, the answer is always "infinitely many solutions."
9. How do you represent a linear equation graphically?
Instruction: Represent a linear equation in two variables on a graph by finding at least two solution points and then drawing a straight line that passes through them.
Why it matters: A graph provides a clear visual representation of all the infinite solutions for the equation. Every single point on the line is a solution, making it a powerful tool for understanding the variable relationship.
Steps:
- Find at least two solutions (ordered pairs, (x, y)) for the equation. Finding a third point is a good way to check for errors.
- Draw the x-axis and y-axis on graph paper and choose an appropriate scale.
- Plot the solution points you found on the Cartesian plane.
- Use a ruler to draw a single straight line that passes through all the plotted points.
Tip: The easiest points to find are often the intercepts. Set x=0 to find the y-intercept, and set y=0 to find the x-intercept.
Find at least two (x, y) solution pairs, plot them on a graph, and connect them with a straight line.
10. What is the best way to practise using the NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2?
Instruction: The NCERT Solutions are best used as a verification and learning tool after you have sincerely attempted the problems yourself.
Why it matters: This active learning method strengthens your problem-solving skills. Passively reading solutions can create a false sense of confidence without building the ability to solve questions independently during an exam.
Steps:
- Read the question from the NCERT textbook or the solutions page.
- Close the solution and try to solve the problem from scratch in your notebook.
- If you get stuck, refer to the solution for a hint on the next step, then try to continue on your own.
- Once you have a final answer, compare it with the detailed solution to check both the result and your method.
Check: After using the solutions to understand a problem, try solving a similar, unsolved question. If you can do it without help, you have understood the concept.
