ALL EXPERIMENTS

Pair of Linear Equations in Two Variables

Interactive Visual Lab — Class 10 · Chapter 3

📈 Graphical Method of Solution

A pair of linear equations in two variables represents two straight lines.
  • Intersecting lines → Unique solution (consistent)
  • Coincident lines → Infinitely many solutions (dependent / consistent)
  • Parallel lines → No solution (inconsistent)

Equation 1

x + y + = 0

Equation 2

x + y + = 0
Ex 1: x+3y=6, 2x-3y=12 Ex 2: Parallel lines Ex 3: Coincident Quiz: 10 students Pens & Pencils

⚖️ Consistency Conditions

For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, compare the ratios:
  • a₁/a₂ ≠ b₁/b₂ → Consistent (unique solution)
  • a₁/a₂ = b₁/b₂ = c₁/c₂ → Dependent (infinitely many solutions)
  • a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → Inconsistent (no solution)

Equation 1

x + y + = 0

Equation 2

x + y + = 0

🔄 Substitution Method

Steps:
  1. Find the value of one variable from one equation.
  2. Substitute this value in the other equation.
  3. Solve the resulting single-variable equation.
  4. Substitute back to find the second variable.

Equation 1

x + y + = 0

Equation 2

x + y + = 0
Ex 4: 7x-15y=2, x+2y=3 Aftab's Age Infinitely many No solution

➖ Elimination Method

Steps:
  1. Multiply equations by suitable numbers to make one variable's coefficients equal.
  2. Add or subtract the equations to eliminate that variable.
  3. Solve the resulting single-variable equation.
  4. Substitute back to find the other variable.

Equation 1

x + y + = 0

Equation 2

x + y + = 0
Ex 8: Income Ratio Ex 9: 3x+4y=10 No solution Digits problem

📚 Practice Problems from Textbook

Click on any problem to auto-fill the values in the Graphical, Substitution, or Elimination tabs and solve them interactively.

Exercise 3.1 (i) — Mathematics Quiz

10 students of Class X took part in a quiz. The number of girls is 4 more than the number of boys. Find the number of boys and girls.

x + y = 10, x - y = 4  

Exercise 3.1 (ii) — Pens & Pencils

5 pencils and 7 pens cost ₹50, while 7 pencils and 5 pens cost ₹46. Find the cost of each.

5x + 7y = 50, 7x + 5y = 46  

Example 5 — Aftab and his Daughter

Seven years ago, Aftab was seven times as old as his daughter. Three years from now, he will be three times as old. Find their ages.

s - 7t + 42 = 0, s - 3t - 6 = 0  

Example 10 — Two-Digit Number

Sum of a two-digit number and its reverse is 66. The digits differ by 2. Find the number(s).

x + y = 6, x - y = 2 (or y - x = 2)  

Exercise 3.2 (iii) — Cricket Bats & Balls

7 bats and 6 balls cost ₹3800. 3 bats and 5 balls cost ₹1750. Find cost of each.

7x + 6y = 3800, 3x + 5y = 1750