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Important Questions

Linear Equations in Two Variables

Gujarat Board · Class 9 · Mathematics

Most important questions from Linear Equations in Two Variables for Gujarat Board Class 9 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions24 flashcards5 concepts

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An infographic defining a linear equation in two variables, showing its general form (Ax + By + C = 0) and examples, with labels for variables and coefficients.
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45 Questions·
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Sample Questions

1multiple correct

Which of the following are solutions to 2x - y = 3? (Select all correct answers)

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(2, 1), (0, -3), (1, -1)

Check each option by substituting into 2x - y = 3: (2,1): 2(2) - 1 = 4 - 1 = 3 ✓. (0,-3): 2(0) - (-3) = 0 + 3 = 3 ✓. (1,-1): 2(1) - (-1) = 2 + 1 = 3 ✓. (3,2): 2(3) - 2 = 6 - 2 = 4 ≠ 3. (1,2): 2(1) - 2 = 2 - 2 = 0 ≠ 3.

2multiple choice

If the cost of a notebook is twice the cost of a pen, and notebook costs ₹x and pen costs ₹y, write the linear equation.

Show answer

x = 2y

Given: Cost of notebook = ₹x, Cost of pen = ₹y, Notebook costs twice the pen. Therefore: x = 2 × y, which gives us x = 2y.

3multiple choice

Find the value of x when y = 0 in the equation 3x + 4y = 12.

Show answer

x = 4

Step 1: Substitute y = 0 into 3x + 4y = 12. Step 2: 3x + 4(0) = 12. Step 3: 3x + 0 = 12. Step 4: 3x = 12. Step 5: Divide by 3: x = 4.

4multiple choice

Which of the following equations represent the same line as 2x + 3y = 6?

Show answer

4x + 6y = 12

To find equivalent equations, multiply the original equation by a constant. 2x + 3y = 6, multiplied by 2 gives: 4x + 6y = 12. This represents the same line because every solution of the original equation is also a solution of the new equation.

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Frequently Asked Questions

What are the important topics in Linear Equations in Two Variables for Gujarat Board Class 9 Mathematics?
Key topics in Linear Equations in Two Variables include Decision tree to identify linear equations in two variables, Step-by-step process for converting equations to standard form, Process to verify if an ordered pair is a solution. These are the concepts Gujarat Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Linear Equations in Two Variables — Gujarat Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Linear Equations in Two Variables?
There are 45 practice questions available for Linear Equations in Two Variables. These cover multiple question types including MCQs, short answer, and long answer questions.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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