Consistency from the ratios of coefficients, graphical solutions, and solving by substitution and by elimination, including word problems. Our own step-by-step solutions to Exercises 3.1 to 3.3, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. For \(a_1x + b_1y + c_1 = 0\), \(a_2x + b_2y + c_2 = 0\): \(\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}\) means intersecting lines (one solution); \(\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}\) coincident lines (infinitely many); \(\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \ne \dfrac{c_1}{c_2}\) parallel lines (none).
What it tests. Make one variable the subject of one equation, substitute into the other, solve, then substitute back. If the variables vanish, the lines are coincident (a true statement such as \(3 = 3\)) or parallel (a false one).
What it tests. Multiply the equations so one variable has equal (or opposite) coefficients, add or subtract to eliminate it, solve, then substitute back.
Pair of Linear Equations in Two Variables has 43 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Pair of Linear Equations in Two Variables · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.