NCERT Mathematics, Class 10, textbook pages 24–37

How to help your child with Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables, at home

Solving simultaneous equations, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

solution

NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables: what it teaches

Two unknowns, two conditions. Your teen models situations with two linear equations, solves them graphically and by substitution and elimination, and decides whether a pair has one, none or infinitely many solutions.

Why it matters later. Simultaneous equations are used in coordinate geometry, linear programming and science.

See it: this chapter in pictures

2p + 3n = 110p + 2n = 65p = 25, n = 20
Two conditions, two unknowns.
a₁/a₂ ≠ b₁/b₂ → one solutiona₁/a₂ = b₁/b₂ ≠ c₁/c₂ → noneall equal → infinitely many
Ratios predict the number of solutions.
x + y = 10x − y = 4add: 2x = 14 → x = 7
Add or subtract to eliminate.

You need

  • graph paper
  • price lists for word problems

Tonight’s 45 minutes

  1. 2 pens + 3 notebooks = ₹110; 1 pen + 2 notebooks = ₹65. Write equations.
  2. Solve by elimination: pen ₹25, notebook ₹20.
  3. Graph both lines and see where they meet.
  4. Check consistency using ratios a₁/a₂, b₁/b₂, c₁/c₂.

Words to use

  • linear equation
  • substitution
  • elimination
  • consistent
  • inconsistent
  • graphical method

Watch for

  • Arithmetic slips during elimination. Write each step, and check the answer in both equations.
  • Mixing up parallel and coincident lines. Parallel: no solution; coincident: infinitely many.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youx + y = 10, x − y = 4. Add them?

Your child2x = 14, so x = 7, y = 3.

A game for this week: Price puzzle

  1. Create two-item shopping clues.
  2. The other writes and solves equations.
  3. Check both clues.
  4. Swap roles.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Comparing phone plans.
  • Mixing solutions.
  • Ticket pricing.
  • Speed and distance problems.

Quick check

Ask these at the end of the week. Tap to see the answer.

Solve x + y = 10, x − y = 4.

x = 7, y = 3.

Lines 2x + 3y = 5 and 4x + 6y = 9 are?

Parallel (no solution).

Pen and notebook prices from the example?

₹25 and ₹20.

Ready for the next chapter when your child…

  • Forms pairs of equations from words.
  • Solves by substitution and elimination.
  • Identifies consistency.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

Which method is best?

Elimination when coefficients line up; substitution when one variable is isolated.

What does no solution mean graphically?

Parallel lines.

Is cross-multiplication in the syllabus?

The current book uses graphical, substitution and elimination methods.