Pair of Linear Equations in Two Variables…

✓ Free notes Class 10 Math 1 study file

About these notes

Class 10 Math Pair of Linear Equations in Two Variables explains how to convert word problems into two linear equations and solve them by graphical plotting, substitution, elimination and cross-multiplication; you also get clear topic-wise notes. Main sub-topics: defining variables, forming equations from ages, sums/differences, mixtures and distance problems; graphing two lines (plot two accurate points and choose scale); substitution method; elimination and cross-multiplication methods; classification of solutions using ratios a1/a2, b1/b2, c1/c2; verification by substitution. For CBSE Class 10 students preparing for chapter tests, school exams and board revision; Merit Spring ROH also offers site-wide chapter tests and mock tests for practice.

Key points you will learn

Class 10 Math Pair of Linear Equations in Two Variables notes
Form equations: assign variables, convert sentences to ax + by = c
Graphical method: plot two accurate points per line and mark intersection
Substitution: isolate one variable and substitute into the other equation
Elimination & cross-multiplication: eliminate variables using addition/subtraction or cross-multiplication formula
Solution types using ratios: if a1/a2 ≠ b1/b2 unique; if a1/a2 = b1/b2 ≠ c1/c2 none; if all equal infinitely many
Practice important questions, MCQ and timed chapter test problems; always check by substituting answers back

What is inside this chapter

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Questions students ask

How can I tell if a pair has no solution or infinitely many?

Compare the ratios a1/a2, b1/b2 and c1/c2: if a1/a2 = b1/b2 ≠ c1/c2 the lines are parallel (no solution), and if all three ratios are equal the lines are coincident (infinitely many); verify by attempting substitution.

When should I use the graphical method in exams?

Use the graphical method only when explicitly asked or to visualise intersection; plot two accurate points for each line, use a clear scale and mark the intersection, then verify the coordinates algebraically to avoid plotting errors.

How to form equations from word problems?

Assign variables with units, write algebraic relations for sums, differences, ratios, ages, mixtures or distance, then rearrange into standard form ax + by = c; choose substitution or elimination based on which method simplifies coefficients.

Where to find Class 10 Math Pair of Linear Equations in Two Variables notes and important questions?

Use msroh.in’s Class 10 Math section and search the chapter name to open topic-wise notes; the site also provides chapter tests and mock tests for timed practice and revision.

What's the fastest way to check my answer?

Substitute the found values of x and y into both original equations to confirm correctness; for word problems also check units and reasonableness (ages non-negative, whole quantities where required) and rework algebra if results disagree.

More Math chapters

Real Numbers Polynomials Quadratic Equations Arithmetic Progressions Triangles Coordinate Geometry All chapters →

Class 10 — other subjects

Science Social Science Computer ENGLISH HINDI SANSKRIT

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