# 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