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Simultaneous Equations
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
About the author
Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
x + y = 10 is satisfied by (3,7), (0,10), (5,5) and endless others - a whole line of points. Add a second condition like x − y = 2 and only one pair fits both.
Match the coefficient of one variable (multiply if needed), then add or subtract to remove it. Solve the single variable left, then back-substitute.
Best when a variable already has coefficient 1, like y = 2x − 1. Swap that expression into the second equation to get one unknown.
Different gradients cross once (one solution). Same gradient, different intercept means parallel (no solution). Identical lines mean infinitely many solutions.
Hard words & meanings
| simultaneous | happening at the same time; both equations must be true together |
| variable | an unknown quantity shown by a letter such as x or y |
| coefficient | the number multiplying a variable, e.g. 3 in 3x |
| elimination | adding or subtracting equations to remove one variable |
| substitution | replacing a variable with an equal expression from the other equation |
| intersection | the point where two lines cross on a graph |
| gradient | the steepness of a line; equations with the same gradient are parallel |
| consistent | a system that has at least one solution; inconsistent means none |
Model exam answers, grammar & audio
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