Ganita Manjari · Class 9 · Part II · Chapter 13
Three questions on the standard form ax + by + c = 0: writing an equation from a, b and c, completing a table, and choosing the right equation for a situation.
Brilliant! You have finished every question in this exercise.
Linear equation in two variables: ax + by + c = 0 with a and b not both zero.
Coefficient: the number multiplying a variable.
Constant term: the number with no variable, c.
Multiplying by 5 removes the fraction: 15x − 1 = 0. The variable y is there with coefficient 0, so it is still an equation in two variables.
The equation is 3x − 15 = 0 (or 15x − 1 = 0).
| Equation | Standard form | a | b | c |
|---|---|---|---|---|
| y − 15 = 2x | 2x − y + 15 = 0 | 2 | −1 | 15 |
| 3y − 2x = 0 | −2x + 3y + 0 = 0 | −2 | 3 | 0 |
| 5x = 3y | 5x − 3y = 0 | 5 | −3 | 0 |
| x = 8 | x + 0y − 8 = 0 | 1 | 0 | −8 |
| 3y = 1 | 0x + 3y − 1 = 0 | 0 | 3 | −1 |
Each equation can also be written with all the signs reversed, for example y − 15 = 2x is also −2x + y − 15 = 0 with a = −2, b = 1, c = −15. Both are correct.
The completed table is above: for example x = 8 has a = 1, b = 0, c = −8 and 3y = 1 has a = 0, b = 3, c = −1.
The notebook costs twice the pen, so t is twice p: t = 2p. Test with numbers: a pen at ₹10 gives a notebook at ₹20, and t = 2p gives 20 = 2 × 10 ✓. Meera's p = 2t would make the pen cost twice the notebook, which is the wrong way round.
The runs of the two batsmen are x and y, and together they scored 176. So x + y = 176 is correct. (Since runs are whole numbers from 0 to 176, only some of the solutions of the equation make sense here, for example (100, 76).)
(i) Charlie's t = 2p is correct. (ii) Yes, x + y = 176 is a correct representation.
Always move every term to one side, so the right side is 0.
Source of the questions: NCERT, Ganita Manjari, Grade 9, Part II, Chapter 13, Exercise Set 13.1. The solutions, explanations and diagrams on this page are our own working.