NCERT Ganita Manjari, Class 9, textbook pages 85–122 (Part II)

How to help your child with Class 9 Maths Chapter 13, Two Variables, One Line, at home

Linear equations in two variables and solving pairs, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

(3, 2)60x + 50y = 280x + y = 5

NCERT Class 9 Maths Chapter 13 Two Variables, One Line: what it teaches

Mangoes at ₹60 per kg and bananas at ₹50 per kg costing ₹280 in all give 60x + 50y = 280. Your teen writes linear equations in two variables, graphs them as lines, and solves a pair of equations by graphing, substitution and elimination.

Why it matters later. Pairs of linear equations are central to Class 10 algebra and coordinate geometry.

See it: this chapter in pictures

60x + 50y = 280(x, y) = (3, 2), (0.5, 5)…infinitely many solutions
Solutions form a line.
x + y = 5 → y = 5 − x60x + 50(5 − x) = 280x = 3, y = 2
Replace one variable.
check (3, 2):60·3 + 50·2 = 280 ✓3 + 2 = 5 ✓
Check both equations.

You need

  • graph paper
  • price lists
  • a calculator

Tonight’s 30 minutes

  1. Write the fruit equation 60x + 50y = 280 and find whole-number solutions (x = 3, y = 2).
  2. Draw its graph and check that solutions lie on the line.
  3. Add a second condition: she bought 5 kg in all (x + y = 5). Solve the pair.
  4. Solve the same pair by elimination and compare.

Words to use

  • linear equation
  • two variables
  • solution
  • graph
  • substitution
  • elimination

Watch for

  • Thinking one equation in two variables has one solution. It has infinitely many; they form a line.
  • Arithmetic slips in elimination. Check the answer in both equations.

What it sounds like at home

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

You60x + 50y = 280 and x + y = 5?

Your childReplace y: 60x + 250 − 50x = 280, so x = 3, y = 2.

A game for this week: Two-clue puzzle

  1. Invent a two-item shopping story with two clues.
  2. The other player writes and solves equations.
  3. Check with both clues.
  4. Swap roles.

A 5-day plan, 30 minutes a day

  1. Day 1Write equations from stories.
  2. Day 2Graph a line.
  3. Day 3Solve a pair by graphing.
  4. Day 4Substitution and elimination.
  5. Day 5Two-clue puzzle.

Everyday moments to practise

  • Comparing mobile plans.
  • Shopping puzzles.
  • Ticket sales.
  • Mixing problems.

Quick check

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

One whole-number solution of 60x + 50y = 280?

x = 3, y = 2.

Solve 60x + 50y = 280 and x + y = 5.

x = 3, y = 2.

How many solutions does a single linear equation in two variables have?

Infinitely many.

Ready for the next chapter when your child…

  • Forms linear equations in two variables.
  • Graphs them.
  • Solves pairs of equations.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

Why is the graph a line?

Solutions change at a steady rate, giving a straight line.

Which method is best?

Elimination when coefficients line up; substitution when one variable is easy to isolate.

What if lines are parallel?

There is no common solution.