# NCERT Solution for Linear equation Chapter 4 Exercise 4.2

In this page we have NCERT book Solutions for Class 9th Maths Linear equations in two variables for EXERCISE 4.2 on page 70. Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1
Which one of the following options is true, and why?
$y = 3x + 5$ has
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions
Solution
infinitely many solutions

Question 2
Write four solutions for each of the following equations:
(i) $2x + y = 7$
(ii) $\pi x + y = 9$
(iii) $x = 4y$
Solution
(i) $2x + y = 7$
Taking x =0
y=7
Taking y=0
x= 7/2
Taking x=1
y= 7-2 =5
Taking y=1
x=3
So (0,7) ,( 7/2,0),(1,5) and (3,1) are Four solutions

(ii) $\pi x + y = 9$
Taking x =0
y=9
Taking y=0
$x= \frac {9}{\pi}$
Taking x=1
$y= 9- \pi$
Taking y=1
$x= \frac {8}{\pi}$
So (0,9) ,($\frac {9}{\pi}$,0) ,(1,$9- \pi$) and ($\frac {8}{\pi}$,1) are Four solutions
(iii) $x = 4y$
Taking x =0
y=0
Taking x=1
y= 1/4
Taking y=1
x=4
Taking x=2
x=1/2
So (0,0) ,( 1,1/4),(4,1) and (2,1/2) are Four solutions
Question 3
Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (i) (0, 2)
(ii) (2, 0)
(iii) (4, 0)
(iv) $(\sqrt {2},4 \sqrt {2})$
(v) (1,1)
Solution
i. Putting x=0,y=2
$0 -4 =4$
$-4 \ne 4$
So,This is not the solution

ii. Putting x=2,y=0
$2 -0 =4$
$2 \ne 4$
So,This is not the solution

iii. Putting x=4,y=0
$4 -0 =4$
$4 = 4$
So,This is a solution

iv. Putting $x=\sqrt {2}$,$y=4 \sqrt {2}$
$\sqrt {2} -8 \sqrt {2}=4$
$7\sqrt {2} \ne 4$
So,This is not the solution

v. Putting x=1,y=1
$1 - 2 =4$
$-1 \ne 4$
So,This is a solution

Question 4
Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Solution
Puttinf x=2 and y=1
$4 + 3 =k$
$7=k$
Hence k=7

Reference Books for class 9 Math

Given below are the links of some of the reference books for class 9 Math.

1. Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
2. Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
3. Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
4. Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.

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