RRB Group D · Bite-size lessons

Algebra

About 6 min · Mathematics · English

Time worked out from the lesson's 354 words at 150 words a minute, plus a minute for each question.

Unlike lengthy arithmetic problems, algebra questions test your ability to translate word problems into equations and solve them systematically. Mastery of linear equations, simultaneous equations, and basic identities is essential because these tools underpin many other topics — from age problems to ratio questions.

Key ideas

• Variable and constant: A variable (x, y, z) represents an unknown quantity; a constant is a fixed number. An algebraic expression combines variables and constants using operations.
• Linear equation in one variable: An equation of the form ax + b = 0, where a ≠ 0. It has exactly one solution: x = -b/a. The degree (highest power of the variable) is 1.
• Simultaneous linear equations: Two equations in two variables (x and y) that must both be true at the same time. Standard form: a₁x + b₁y = c₁ and a₂x + b₂y = c₂. They usually have one unique solution unless the lines are parallel or coincident.
• Substitution method: Solve one equation for one variable, then substitute that expression into the other equation. Useful when one equation is already isolated or easy to isolate.
• Elimination method: Multiply equations by suitable numbers so that adding or subtracting them cancels one variable. Often faster than substitution when coefficients align nicely.

Quick reference

• One-variable linear: ax + b = c ⟹ x = (c − b)/a in one step.
• Simultaneous: Use elimination if coefficients are neat; substitution if one variable is isolated.
• (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b² — memorise these three.
• Always verify your solution by substituting back into the original equation(s).
• Word problems: Define variables clearly, translate every sentence into an equation, then solve systematically.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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