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Linear Equations in Two Variables

Gujarat Board · Class 9 · Mathematics

Flashcards for Linear Equations in Two Variables — Gujarat Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

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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24 Flashcards
Card 1Definition and Identification of Linear Equations

Identify which of the following is a linear equation in two variables: (i) 2x + 3y = 5, (ii) x² + y = 4, (iii) 3x + 2y + z = 6

Answer

Answer: (i) 2x + 3y = 5 is a linear equation in two variables. Step 1: Check if equation is in form ax + by + c = 0 where a and b are not both zero. Step 2: For (i): 2x + 3y - 5 = 0. This has variabl…

Card 2Converting Equations to Standard Form

Express 3y = 2x - 7 in the form ax + by + c = 0 and identify a, b, and c.

Answer

Step 1: Start with 3y = 2x - 7 Step 2: Move all terms to one side: 2x - 3y - 7 = 0 (or -2x + 3y + 7 = 0) Step 3: Rearrange in standard form: 2x - 3y - 7 = 0 Step 4: Compare with ax + by + c = 0 Answe…

Card 3Verifying Solutions

Check if (2, 1) is a solution of the equation 2x + y = 5. Show your working.

Answer

Step 1: Substitute x = 2 and y = 1 into the equation 2x + y = 5 Step 2: Left side = 2(2) + 1 = 4 + 1 = 5 Step 3: Right side = 5 Step 4: Since Left side = Right side (5 = 5), the equation is satisfied …

Card 4Finding Unknown Coefficients

Find the value of k if (1, 2) is a solution of kx + 3y = 7.

Answer

Step 1: Substitute x = 1 and y = 2 into kx + 3y = 7 Step 2: k(1) + 3(2) = 7 Step 3: k + 6 = 7 Step 4: Solve for k by subtracting 6 from both sides Step 5: k = 7 - 6 = 1 Answer: k = 1 Verification: S…

Card 5Finding Multiple Solutions

Find three different solutions of the equation x + 2y = 6.

Answer

Method: Choose values for x and find corresponding y values. Solution 1: Let x = 0 Step 1: 0 + 2y = 6 Step 2: 2y = 6 Step 3: y = 3 Solution: (0, 3) ✓ Solution 2: Let x = 2 Step 1: 2 + 2y = 6 Step 2:…

Card 6Concept of Infinite Solutions

Why does a linear equation in two variables have infinitely many solutions? Explain with an example.

Answer

Reason: A linear equation in two variables has one equation but two unknowns. This underdetermined system allows infinite solutions. Example: Consider 2x + y = 5 Explanation: - We can choose ANY val…

Card 7Word Problems and Equation Formulation

Write a linear equation in two variables for: 'The cost of a notebook is twice the cost of a pen.' (Notebook = x, Pen = y)

Answer

Step 1: Identify the relationship: Cost of notebook = 2 × Cost of pen Step 2: Use variables: x = cost of notebook, y = cost of pen Step 3: Translate to equation: x = 2y Step 4: Rearrange to standard f…

Card 8Verifying Multiple Solutions

Check which of these pairs are solutions of 3x - y = 9: (i) (3, 0), (ii) (2, 3), (iii) (4, 3), (iv) (0, 9)

Answer

We substitute each pair into 3x - y = 9: (i) (3, 0): 3(3) - 0 = 9 - 0 = 9 ✓ SOLUTION (ii) (2, 3): 3(2) - 3 = 6 - 3 = 3 ≠ 9 ✗ NOT a solution (iii) (4, 3): 3(4) - 3 = 12 - 3 = 9 ✓ SOLUTION (iv) (0, …

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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 flashcards are available for Linear Equations in Two Variables?
There are 24 flashcards for Linear Equations in Two Variables covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

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