NCERT Class 10th Mathematics
18

NCERT Class 10th – Chapter 3 – Exercise 3.2 Pair of Two Equations in Two Variables

NCERT full solutions  here you can find full detailed solutions for all the questions  with proper format. class 10 maths ncert solutions chapter 3 exercise 3.2.

You can see the solution for complete chapter here –

EXERCISE -3.2

QUE:- 1. Form the pair of linear equations in the following problems, and find their solutions

           graphically.
         (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4
         more than the number of boys, find the number of boys and girls who took part in
         the quiz.
        (ii) 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together

        cost ` 46. Find the cost of one pencil and that of one pen.

   SOL:-

(i) let the number of girls = x

and let the numbers of boys =y

total number of students =10

therefore , x +y = 10……………(1)

according to quetion , number of girl 4is more than number of boys  so

x=y+4      …………………….(2)

to represent graphically ,three solution of each equation is needed.

to represent graphicaly , three solution of each equation is needed.

from the equation (1) we get

x= 10-y

x 5 4 6
y 5 6 4

from the equation (2) , we get

x= y +4

x 5 4 3
y 1 0 -1

(ii)

let the cost of one pencil =x rs and let the cost of one pen = y rs

according to first condition

5x+7y =50……………..(1)

according to second condition

7x +5y =46……………….(2)

to represent graphically three solutions of each equation is given below ,

from the equation (1) , we get

x= (50-7y)/5

x 3 10 -4
y 5 0 10

from the equation (2) , we get

x=(46 -5y)/7

x 8 3 -2
y -2 5 12

QUE :-2 On compairing  the ratio a1/a2,b1/b2, and c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point , are parallel or cioncident:

    (i) 5x 4y +8 =0

       7x + 6y -9 =0

    (ii) 9x +3y +12 =0

         18 x +6y +24 = 0

    (iii) 6x -3y =10=0

       2x  -y = 9 =0

SOL:- 

(i) 5x 4y +8 =0

7x + 6y -9 =0

here, a1/a2 =5/7,b1/b2 =-4/6=-2/3

⇒ a1/a2 ≠ b1/b2 ,so , the following pairs of linear equations intersect at a point.

(ii) 9x +3y +12 =0

18 x +6y +24 = 0

here , a1/a2 =9/18=1/2,b1/b2=3/6=1/2,c1/c2 =12/24=1/2

⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coincident.

(iii) 6x -3y =10=0

2x  -y = 9 =0

here , a1/a2 =6/2=3/1,b1/b2=-3/-1=3/1,c1/c2 =10/9

⇒ a1/a2 =b1/b2 ≠ c1/c2 , so the following pairs of linear equation are parallel.

QUE :-3 On compairing  the ratio a1/a2,b1/b2, and c1/c2 find out whether the  following pairs of linear equations are consistence , or inconsistent :

(i) 3x +2y =5 ; 2x -3y =7    (ii) 2x -3y =8 ; 4x+6y =9

(iii) (3/2)x +(5/3)y =7 ;9x -10y =14 (iv) 5x -3y =11; -10x+6y =-22

(v) 4/3x+2y =8 ; 2x +3y = 12

SOL:-

(i) 3x +2y =5

    2x -3y =7

here , a1/a2 =3/2,b1/b2=2/-3=1/2,c1/c2 =12/24=1/2

⇒ a1/a2 ≠b1/b2  , so the following pairs of linear equation are coinsistent.

 (ii) 2x -3y =8

   4x -6y =9

here , a1/a2 =2/4=1/2 ,b1/b2=-3/-6=1/2,c1/c2 =8/9

⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.

(iii) 3/2x +5/3y =7

    9x -10y =14

here , a1/a2 =(3/2)/9=1/6,b1/b2=(5/3)/-10=-1/6

⇒ a1/a2 ≠b1/b2  , so the following pairs of linear equation are coinsistent.

(iv) 5x -3y =11

    -10x +6y =-22

here , a1/a2 =5/-10=-1/2,b1/b2=-3/6=-1/2,c1/c2 =11/22=-1/2

⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.

(v) 4/3x +2y =8

    2x +3y =12

here , a1/a2 =(4/3)/2=2/3,b1/b2=2/3,c1/c2 =8/12=2/3

⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.

QUE:-4 Which of the following pairs of linear equations are consistent/inconsistent? If
           consistent, obtain the solution graphically:

         (i) x + y = 5, 2x + 2y = 10
         (ii) x – y = 8, 3x – 3y = 16
         (iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
         (iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

SOL :-

 (i) x + y = 5,

   2x + 2y = 10

a1/a2 =1/2,b1/b2=1/2,c1/c2 =5/10=1/2

⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.

for three solutions of each equation,

from equation (1)

x=5-y

x 4 3 2
y 1 2 3

from equation (2)

x= (10-2y)/2

x 4 3 2
y 1 2 3

graph que 4 (i)

que 4 (i)

(ii) x – y = 8,

3x – 3y = 16

a1/a2 =1/3,b1/b2=1/3,c1/c2 =8/16=1/2

⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.

(iii) 2x + y – 6 = 0,

4x – 2y – 4 = 0

a1/a2 =2/4=1/2,b1/b2=1/-2,

⇒ a1/a2 ≠b1/b2  , so the following pairs of linear equation are coinsistent/inconsistent.

from equation (1) we get

x= 6-y/2

x 0 1 2
y 6 4 2

from equation (2) we get

x= 4+2y/4

x 1 2 3
y 0 2 4

que.4 (iii)

(iv) 2x – 2y – 2 = 0,

4x – 4y – 5 = 0

a1/a2 =2/4=1/2,b1/b2=-2/-4=1/2,c1/c2 =-2/-5=2/5

⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.

QUE:-5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is
            36 m. Find the dimensions of the garden.

SOL:-

let breadth(B) of garden= x meter

let length(L) of gaeden = y meter

half of perimeter =36 meter

so 1/2[2(x+y)]=36

x +y =36     ……………….(1)

according to the question L is 4 meter more than B so,

y = x + 4

to get 3 solution of each equation

from equqtion (1)

x =36 – y

x 0 36 16
y 36 0 20

from equqtion (2)

y = x + 4

x 0 8 12
y 4 8 16

graph of que.5

both the lines intersect at (16,20 ).

so the B of garden is 16 meter and L of garden is 20 meter .

QUE:-6 Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables
            such that the geometrical representation of the pair so formed is:
           (i) intersecting lines               (ii) parallel lines              (iii) coincident lines

SOL:-

(i)  given line 2x + 3y-8 =0 is intersect the line x + y -10=0

a1/a2 ≠b1/b2

(ii)  given line  2x + 3y-8 =0 is parallel to 4x +6y – 9 =0

a1/a2 =b1/b2 ≠c1/c2

(iii) given line  2x + 3y-8 =0 is coincident to 4x + 6y -16 =0

a1/a2 =b1/b2 =c1/c2

QUE7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the
           coordinates of the vertices of the triangle formed by these lines and the x-axis, and
            shade the triangular region.

SOL:-

       x – y + 1 = 0 ……………………(1)

       3x + 2y – 12 = 0 ………………..(2)

equation (1) we get  x = y -1

x 0 1 2
y 1 2 3

equation (2) we get x=(12-2y)/3

 

x 4 2 0
y 0 3 6

graph of que.7

the cordinates of the verticle of the triangle formed by tjese lines and the x- axis are

(-1 ,0 ) , (4 , 0) and ( 2,3)

You can see the solution for complete chapter here –

Tags – class 10th maths solutions, maths solution for class 10, 10th class maths solution, mathematics solution class 10th, maths solution, 10th class maths , mathematics for class 10, chapter 3 solution in maths.

Related Posts