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Pair of Linear Equations in Two Variables

Gujarat Board · Class 10 · Mathematics

Flashcards for Pair of Linear Equations in Two Variables — Gujarat Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions25 flashcards5 concepts

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Card 1Substitution Method

Solve the pair of equations using substitution method: y = 2x + 1 3x + y = 11

Answer

Step 1: We have y = 2x + 1 from the first equation. Step 2: Substitute this value of y into the second equation: 3x + (2x + 1) = 11 Step 3: Simplify: 5x + 1 = 11 Step 4: Solve for x: 5x = 10 → x = 2 S…

Card 2Elimination Method

Solve using the elimination method: 2x + 3y = 13 5x - 3y = 8

Answer

Step 1: Observe that the coefficients of y are +3 and -3 (opposites). Step 2: Add both equations to eliminate y: (2x + 3y) + (5x - 3y) = 13 + 8 Step 3: Simplify: 7x = 21 Step 4: Solve for x: x = 3 Ste…

Card 3Consistency and Nature of Solutions

Determine if the pair of equations is consistent, inconsistent, or dependent: 3x + 4y = 12 6x + 8y = 24

Answer

For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, rewrite: 3x + 4y - 12 = 0 6x + 8y - 24 = 0 Calculate the ratios: a₁/a₂ = 3/6 = 1/2 b₁/b₂ = 4/8 = 1/2 c₁/c₂ = -12/-24 = 1/2 Since a₁/a₂ = b₁/b…

Card 4Consistency and Nature of Solutions

Check whether the lines represented by these equations are intersecting, parallel, or coincident: x + 2y = 4 2x + 4y = 12

Answer

Rewrite in standard form: x + 2y - 4 = 0 2x + 4y - 12 = 0 Calculate the ratios: a₁/a₂ = 1/2 b₁/b₂ = 2/4 = 1/2 c₁/c₂ = -4/-12 = 1/3 Observation: a₁/a₂ = b₁/b₂ ≠ c₁/c₂ (since 1/2 ≠ 1/3) Answer: The l…

Card 5Elimination Method

Solve the pair of equations: 2x + y = 7 x - y = 2

Answer

Using the elimination method (y coefficients are opposite: +1 and -1): Step 1: Add both equations: (2x + y) + (x - y) = 7 + 2 Step 2: Simplify: 3x = 9 Step 3: Solve for x: x = 3 Step 4: Substitute x …

Card 6Real-World Applications

Akhila spent ₹20 at a fair. She had rides on a Giant Wheel (₹3 each) and played Hoopla (₹4 each). The number of Hoopla games is half the number of rides. Find how many rides and games she had.

Answer

Step 1: Define variables Let x = number of rides on Giant Wheel Let y = number of Hoopla games Step 2: Set up equations from the given information Equation 1 (money spent): 3x + 4y = 20 Equation 2 (r…

Card 7Elimination Method with Multiplication

Solve by elimination method with multiplication: 3x + 2y = 8 2x + 3y = 7

Answer

Step 1: Observe that no coefficients are directly opposite. We need to multiply to make them so. Step 2: To eliminate x, multiply first equation by 2 and second by 3: First equation × 2: 6x + 4y = 16 …

Card 8Graphical Method - Understanding

When do you use the graphical method to solve a pair of linear equations? What are its advantages and limitations?

Answer

The graphical method involves plotting both equations as lines on a coordinate plane. When to use it: • When you want to visualize the relationship between the equations • When the solution values ar…

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What are the important topics in Pair of Linear Equations in Two Variables for Gujarat Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Pair of Linear Equations — Complete Chapter Overview, Decision Tree: Which Method to Use for Solving Linear Equations, Chapter Overview: Pair of Linear Equations in Two Variables. These are the concepts Gujarat Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Pair of Linear Equations in Two Variables — Gujarat Board Class 10 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.
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There are 25 flashcards for Pair of 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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