Question

1. Form the pair of linear equations in the following problems, and find their solutions
graphically.
(1) 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.
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Answer 1

Answer:

1.Let number of boys be x.

Number of girls be y.

Given that total number of student is 10 so that

x+y=10

Subtract y both side we get

x=10–y

Plug y=0,5,10 we get

x=10–0=10

x=10–5=5

x=10–10=0

Therefore, the required points are (0,10),(5,5),(10,0).

Given that If the number of girls is 4 more than the number of boys

So that

y=x+4

Plug x=−4,0,4, and we get

y=−4+4=0

y=0+4=4

y=4+4=8

Therefore, the required points are (−4,0),(0,4),(4,8).

The graph is as shown above:

Since the point of intersection in the above graph is (3,7),

Hence, the number of boys are 3 and the number of girls are 7.

solution

2.let cost(in RS) of one pencil = x

cost (in RS) of one pen = y

Therefore , according to question

5x+7y = 50 ........ (1)

7x + 5y = 46 .........(2)

Multiply equation 1 by 7

equation by 5 we get

7(5x+7y)= 7*50

35x +49y = 350 .......(3)

5(7x +5y) = 5*46

35x +25y = 230 ....... (4)

Subtract equation 4 from equation 3 , we get

35x + 49y - 35x - 25y= 350 -230

49y -25y = 120

24y = 120

y = 120 /24

y= 5

Substitute y=5 in equation 1 , we get

5x + 7*5 =50

5x+35 =50

5x = 50 - 35

5x =15

x= 15/5

x=3

Hence

Cost of One Pencil = x =3

Cost of One Pen =y =5

Answer 2

Answer:

i) let the no. og girls be x and no. of boys be y

A.T.Q.

X + Y = 10 _____(1)

X = Y + 4 ______(2)

Sol. for eq. 1

x = 4 | 2 | 6

y = 6 | 8 | 4

Sol. for eq. 2

x = 10 | 6 | 8

y = 6 | 2 | 4

Mark all these co ordinates on graph for both the ea. and the point where the line will inter sect will be ( 7 , 3 )

=> no. of girls = 7 = x

no. of boys = 3 = y

ii) let the cost of 1 pen be rupees x

and the cost of one pencil be rupees y

5x + 7y = 50 _____(1)

7x +5y = 46 _____(2)

Sol. for eq. 1

x = 4 | -3 | -16

y = 10 | 5 | -5

Mark these co ordinates on graph and the point where the line will intersect will be (-3 , 5)

= > X = - 3

Y = 5

HOPE THIS HELPS YOU...