SATHEE: Chapter 04 Linear Equations in Two Variables Exercise-01

Chapter 04 Linear Equations in Two Variables Exercise-01

EXERCISE 4.1

1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be ₹ $x$ and that of a pen to be ₹ $y$ ).

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Solution

Let the cost of a notebook and a pen be $x$ and $y$ respectively.

Cost of notebook $= 2 \times$ Cost of pen $x = 2 y x - 2 y = 0$

2. Express the following linear equations in the form $a x + b y + c = 0$ and indicate the values of $a, b$ and $c$ in each case:

(i) $2 x + 3 y = 9.3 \overset{―}{5}$

(ii) $x - \frac{y}{5} - 10 = 0$

(iii) $- 2 x + 3 y = 6$

(iv) $x = 3 y$

(v) $2 x = - 5 y$

(vi) $3 x + 2 = 0$

(vii) $y - 2 = 0$

(viii) $5 = 2 x$

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Solution

$\begin{aligned} (i) 2 x + 3 y = 9.3 \overset{―}{5} \\ \Rightarrow 2 x + 3 y - 9.3 \overset{―}{5} \end{aligned}$

Comparing the equation with $ax + by + c = 0$

$a = 2, b = 3, c = - 9.3 \overset{―}{5}$

(ii) $x - \frac{y}{5} - 10 = 0$

Comparing the equation with $a x + b y + c = 0$

$a = 1, b = - \frac{1}{5}, c = - 10$

$\begin{aligned} (iii) - 2 x + 3 y = 6 \\ \Rightarrow - 2 x + 3 y - 6 = 0 \end{aligned}$

Comparing the equation with $a x + b y + c = 0$

$a = - 2, b = 3, c = - 6$

(iv) $x = 3 y$

$\Rightarrow x - 3 y = 0$

Comparing the equation with $ax + by + c = 0$

$a = 1, b = - 3, c = 0$

(v) $2 x = - 5 y$

$\Rightarrow 2 x + 5 y = 0$

Comparing the equation with $ax + by + c = 0$

$a = 2, b = 5, c = 0$

$\begin{aligned} (vi) 3 x + 2 = 0 \\ \Rightarrow 3 x + 0 y + 2 = 0 \end{aligned}$

Comparing the equation with $ax + by + c = 0$

$a = 3, b = 0, c = 2$

(vii) $y - 2 = 0$

$\Rightarrow 0 x + y - 2 = 0$

Comparing the equation with $a x + b y + c = 0$

$a = 0, b = 1, c = - 2$

(viii) $5 = 2 X$

$\Rightarrow - 2 x + 0 y + 5$

Comparing the equation with $ax + by + c = 0$

$a = - 2, b = 0, c = 5$

Chapter 04 Linear Equations in Two Variables Exercise-01

EXERCISE 4.1

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Chapter 04 Linear Equations in Two Variables Exercise-01

EXERCISE 4.1

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

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