Pair of Linear Equations in Two Variables — Flashcards
Punjab Board · Class 10 · Mathematics
30 flashcards for Pair of Linear Equations in Two Variables (Punjab Board Class 10 Mathematics) to test yourself on key terms and facts.
Interactive on Super Tutor
Studying Pair of Linear Equations in Two Variables? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
Free trial, no card needed.
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Pair of Linear Equations in Two Variables.
Solve by substitution method: x + y = 10 and x - y = 2
Answer
Step 1: From first equation, express x in terms of y: x = 10 - y Step 2: Substitute in second equation: (10 - y) - y = 2 Step 3: Simplify: 10 - 2y = 2 Step 4: Solve for y: 2y = 8, so y = 4 Step 5: Sub…
Solve by elimination method: 2x + 3y = 13 and 3x - 2y = 4
Answer
Step 1: Multiply first equation by 2: 4x + 6y = 26 Step 2: Multiply second equation by 3: 9x - 6y = 12 Step 3: Add equations to eliminate y: (4x + 9x) + (6y - 6y) = 26 + 12 Step 4: Simplify: 13x = 38,…
When should you use the substitution method instead of elimination method?
Answer
Use substitution method when: 1. One equation is already solved for one variable (like y = 2x + 5) 2. One variable has coefficient 1 or -1 (easy to isolate) 3. Coefficients are small and don't need mu…
Determine the nature of lines: Compare ratios a₁/a₂, b₁/b₂, c₁/c₂ for equations: 2x + 3y = 7 and 4x + 6y = 15
Answer
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 Given: 2x + 3y - 7 = 0 and 4x + 6y - 15 = 0 Step 1: Calculate ratios: a₁/a₂ = 2/4 = 1/2 b₁/b₂ = 3/6 = 1/2 c₁/c₂ = -7/-15 = 7/15 Step 2: Compare …
Solve the system: 7x - 15y = 2 and x + 2y = 3
Answer
Using Substitution Method: Step 1: From second equation, isolate x: x = 3 - 2y Step 2: Substitute in first equation: 7(3 - 2y) - 15y = 2 Step 3: Expand: 21 - 14y - 15y = 2 Step 4: Combine like terms: …
Akhila spent ₹20 total. Rides on Giant Wheel cost ₹3 each, Hoopla costs ₹4 per game. She played Hoopla half as many times as rides. Find number of rides and games.
Answer
Step 1: Define variables. Let x = number of rides, y = number of Hoopla games Step 2: Form equations: Condition 1: y = x/2 (Hoopla times = half the rides) Condition 2: 3x + 4y = 20 (total cost) Step 3…
Check if this pair has infinitely many solutions: 5x - 8y + 1 = 0 and 10x - 16y + 2 = 0
Answer
Step 1: Compare coefficients. Rewrite second equation by dividing by 2: 5x - 8y + 1 = 0 Step 2: Notice that both equations become identical when second is divided by 2. Step 3: Check ratios: a₁/a₂ = 5…
Solve by elimination: 3x + 4y = 10 and 2x - 2y = 2
Answer
Step 1: Make coefficients of y equal. Multiply first equation by 1 and second by 2: 3x + 4y = 10 4x - 4y = 4 Step 2: Add equations to eliminate y: (3x + 4x) + (4y - 4y) = 10 + 4 7x = 14 x = 2 Step 3: …
+22 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Pair of Linear Equations in Two Variables for Punjab Board Class 10 Mathematics?
How many flashcards are available for Pair of Linear Equations in Two Variables?
How should I revise Pair of Linear Equations in Two Variables for the Punjab Board Class 10 board exam?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Pair of Linear Equations in Two Variables
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Syllabus
What topics to cover
For serious students
Get the full Pair of Linear Equations in Two Variables chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Punjab Board Class 10 Mathematics. Free to start, no card needed.