NCERT Solutions for Class 9 Maths Chapter 13 — Exercise Set 13.1#
A linear equation in two variables in standard form is
$$ax + by + c = 0$$where $a$, $b$, $c$ are real numbers and $a$, $b$ are not both zero. $a$ is the coefficient of $x$, $b$ the coefficient of $y$, and $c$ the constant term.
1. Write a linear equation in two variables in which a = 3, b = 0 and c = −1/5. #
Solution
Substituting in $ax + by + c = 0$:
$$3x + 0 \cdot y - \dfrac{1}{5} = 0$$That is, $3x - \dfrac{1}{5} = 0$ (with $y$ having coefficient 0).
2. Complete the following table after expressing the given linear equations in standard form. #
Solution
We move every term to the left-hand side so that the right-hand side is 0.
| Linear equation | Standard form | Coefficient of $x$ | Coefficient of $y$ | Constant term |
|---|---|---|---|---|
| $y - 15 = \sqrt{2}x$ | $\sqrt{2}x - y + 15 = 0$ | $\sqrt{2}$ | $-1$ | $15$ |
| $3y - 2x = 0$ | $-2x + 3y + 0 = 0$ | $-2$ | $3$ | $0$ |
| $5x = 3y$ | $5x - 3y + 0 = 0$ | $5$ | $-3$ | $0$ |
| $x = 8$ | $x + 0 \cdot y - 8 = 0$ | $1$ | $0$ | $-8$ |
| $3y = 1$ | $0 \cdot x + 3y - 1 = 0$ | $0$ | $3$ | $-1$ |
(Multiplying a standard form by $-1$ also gives a correct standard form, e.g. $2x - 3y = 0$ for the second row, with all signs changed.)
3. (i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct? (ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation? #
(i) Notebook and pen
The notebook costs twice as much as the pen, so the notebook’s cost $t$ equals 2 times the pen’s cost $p$:
$$t = 2p$$∴ Charlie is correct. Meera’s $p = 2t$ would mean the pen costs twice as much as the notebook. (Check: a ₹10 pen and ₹20 notebook satisfy $t = 2p$ but not $p = 2t$.)
(ii) Runs scored
Yes. The two batsmen’s runs $x$ and $y$ add up to 176, so
$$x + y = 176$$is a correct linear equation for the situation (in standard form, $x + y - 176 = 0$).