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Two equations, two letters, one shared answer. Sometimes there is none.

This is Chapter 3, Pair of Linear Equations in Two Variables. It is in your NCERT Maths book. A variable is a letter for an unknown number.

What you will learn

• The pair and its picture. Two lines cross, run parallel, or match.
• A story becomes a pair. Name the letters, then write two equations.
• Three ratios. They give the verdict before you draw.
• Zoom out. A small sketch can hide a crossing.
• Tidy an equation. Remove fractions and brackets. The line does not change.
• Two methods. Substitute a letter, or cancel one. Then find the other.
• Two odd endings. 0 = 0 and a false sentence.
• Read the answer back. Can the story allow it?
• Draw and read. Two points per line. The crossing is the answer.

Need a quick recap?

These Class 9 lessons help. If one feels hard, open it first.

• Two letters, one claim — what a linear equation in two variables is.
• Where two lines meet — the graphical method, and its honest limit.
• The three things two lines can do — cross, run parallel, or coincide.
• The substitution walk — naming a bare letter and using it.
• Scale the equations, then take one away — elimination by matching coefficients.
• What falls out when nothing is left — the 0 = false and 0 = 0 endings.