NCERT Solutions for Class 9 Maths Ganit Manjari Chapter 4 Exercise 4.1

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

Ans
Let the cost of a notebook and a pen be x and y respectively.
Since, cost of a notebook = 2 x cost of a pen
x = 2y or x – 2y = 0
Which is required linear equation.

Q.2

$\begin{array}{l}\text{Express the following linear equations in the form}\\ \text{ax\hspace{0.17em}+\hspace{0.17em}by\hspace{0.17em}+\hspace{0.17em}c\hspace{0.17em}=\hspace{0.17em}0 and indicate the values of \hspace{0.17em}\hspace{0.17em}a,b\hspace{0.17em}\hspace{0.17em}and c in}\\ \text{each case:}\\ \left(\text{i}\right)2\mathrm{x}+3\mathrm{y}=9.3\overline{5}\left(\text{ii}\right)\mathrm{x}-\frac{\mathrm{y}}{5}-10=0\left(\text{iii}\right)-2\mathrm{x}+3\mathrm{y}=6\\ \left(\text{iv}\right)\mathrm{x}=3\mathrm{y}\left(\text{v}\right)2\mathrm{x}=-5\mathrm{y}\left(\text{vi}\right)3\mathrm{x}+2=0\\ \left(\text{vii}\right)\mathrm{y}-2=0\left(\text{viii}\right)5=2\mathrm{x}\end{array}$

Ans

\begin{array}{l}\left(\text{i}\right)2x+3y=9.3\overline{5}\\ \text{or}2x+3y-9.3\overline{5}=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a = 2, b = 3 and c =}-9.3\overline{5}\\ \left(\text{ii}\right)x-\frac{y}{5}-10=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a = 1, b =}-\frac{1}{5}\text{and c =}-10\\ \left(\text{iii}\right)-2x+3y=6\\ \text{or}-2x+3y-6=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a =}-2\text{, b =}3\text{and c =}-6.\\ \left(\text{iv}\right)x=3y\\ \text{or}x-3y=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a =}1\text{, b =}-3\text{and c =}0.\\ \left(\text{v}\right)2x=-5y\\ \text{or}2x+5y=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a}=2\text{, b}=5\text{and c}=0.\\ \left(\text{vi}\right)3x+2=0\\ \text{or 3x}+0.y+2=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a}=3\text{, b}=0\text{and c}=2.\\ \left(\text{vii}\right)y-2=0\\ \text{or 0}\text{.x}+y-2=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a}=0\text{, b}=1\text{and c}=-2.\\ \left(\text{viii}\right)5=2x\\ \text{or}2x+0.y-5=0\\ \text{Comparing with ax + by + c = 0, we get}\\ \text{a}=2\text{, b}=0\text{and c}=-5.\end{array}