Pair of Linear Equations in Two Variables — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Pair of Linear Equations in Two Variables" — 9 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Pair of Linear Equations in Two Variables" — 9 important questions with detailed a…

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Key Questions Covered:

  1. Define a linear equation in two variables and state the general form.
  2. A pair of linear equations is consistent if which condition is satisfied?
  3. Solve the system of equations 2x + y = 7 and x - y = 2 using the elimination …
  4. + 6 more questions in the full chapter

Solutions Summary:

Question Status
Define a linear equation in two variables and state the g… ✓ Solved
A pair of linear equations is consistent if which conditi… ✓ Solved
Solve the system of equations 2x + y = 7 and x - y = 2 us… ✓ Solved

Showing 3 of 9 questions

Q1: Define a linear equation in two variables and state the general form.

Linear Equation in Two Variables: A linear equation in two variables is an equation of the form ax + by + c = 0, where a, b, and c are real numbers and at least one of a or b is non-zero. General form: ax + by + c = 0 or ax + by = c where a = coefficient of x b = coefficient of y c = c...

Q2: A pair of linear equations is consistent if which condition is satisfied?

Consistency of a Pair of Linear Equations: Consider the pair: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 The pair of equations is CONSISTENT if it has at least one solution. Two cases of consistency: 1) Consistent and Independent: Condition: a₁/a₂ ≠ b₁/b₂ Number of solutions: Exactly one (u...

Q3: Solve the system of equations 2x + y = 7 and x - y = 2 using the elimination method.

Given equations: 2x + y = 7 ... (1) x - y = 2 ... (2) Step 1: Add equations (1) and (2) to eliminate y (2x + y) + (x - y) = 7 + 2 3x = 9 x = 3 Step 2: Substitute x = 3 into equation (2) 3 - y = 2 y = 1 Step 3: Verification Substitute x = 3, y = 1 into equation (1): 2(3) + 1 = 6 + 1 = 7 ✓ Substi...

Showing 3 of 9 questions. Visit the full page for complete solutions.