Pair of Linear Equations in Two Variables
Uttarakhand Board · Class 10 · Mathematics
Flashcards for Pair of Linear Equations in Two Variables — Uttarakhand Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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.
1,000+ Class 10 students started this chapter today
This is just one of 5+ visuals inside Super Tutor's Pair of Linear Equations in Two Variables chapter
Explore the full setWhat is a linear equation in two variables? Give the general form.
Answer
A linear equation in two variables is an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Examples: 2x + 3y - 6 = 0, x - y +…
What is a pair of linear equations in two variables?
Answer
A pair of linear equations in two variables consists of two linear equations involving the same two variables. Example: 2x + 3y = 6 and x - y = 1. The solution is the common values of x and y that sat…
Define consistent pair of linear equations.
Answer
A pair of linear equations that has at least one solution is called a consistent pair. This includes cases with exactly one solution (unique) or infinitely many solutions. Example: x + y = 3 and 2x - …
Define inconsistent pair of linear equations.
Answer
A pair of linear equations that has no solution is called an inconsistent pair. This happens when the lines representing the equations are parallel. Example: x + y = 3 and x + y = 5 (parallel lines, n…
What is a dependent pair of linear equations?
Answer
A dependent pair of linear equations consists of two equations that are equivalent and represent the same line. Such pairs have infinitely many solutions. Example: 2x + 4y = 8 and x + 2y = 4 are depen…
What are the three graphical possibilities when representing a pair of linear equations?
Answer
1. Lines intersect at one point → Unique solution (consistent) 2. Lines are parallel → No solution (inconsistent) 3. Lines coincide (same line) → Infinitely many solutions (dependent/consistent)…
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, what condition gives a unique solution?
Answer
When a₁/a₂ ≠ b₁/b₂, the lines intersect at exactly one point, giving a unique solution. The pair is consistent. Example: x + y = 3 and 2x - y = 0 have different slopes, so they intersect once.
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, what condition gives no solution?
Answer
When a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel with no intersection point. The pair is inconsistent. Example: 2x + 3y = 6 and 4x + 6y = 18 (same slope, different y-intercepts).
+12 more flashcards available
Practice AllFrequently Asked Questions
What are the important topics in Pair of Linear Equations in Two Variables for Uttarakhand Board Class 10 Mathematics?
How to score full marks in Pair of Linear Equations in Two Variables — Uttarakhand Board Class 10 Mathematics?
How many flashcards are available for Pair of Linear Equations in Two Variables?
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
Important Questions
Practice with board exam-style questions
Syllabus
What topics to cover
Revision Notes
Key points for last-minute revision
Study Plan
Step-by-step plan to ace this chapter
Formula Sheet
All formulas in one place
Chapter Summary
Understand the chapter at a glance
Practice Quiz
Test yourself with a quick quiz
Concept Maps
See how topics connect visually
For serious students
Get the full Pair of Linear Equations in Two Variables chapter — for free.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Uttarakhand Board Class 10 Mathematics.