Question

The pair of Intersecting lines in the following are.
A. x-2y=0
3x+4y=20
B. x + 3y = 6
2x - 3y = 1
C. y=2x-2
y = 4x-4
D. x + 2y = 4
2x+4y = 12​

Answer 1

Answer:

Exercise 3.1

1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Ans. Let the present age of Aftab = x

And, present age of his daughter is represented as = y

Seven years ago,

Aftab’s age = x – 7

Age of Aftab’s daughter = y – 7

According to the question,

(x – 7) = 7 (y – 7 )

x – 7 = 7 y – 49

x – 7y = – 49 + 7

x – 7y = – 42 … (i)

x = 7y – 42

Putting y = 5, 6 and 7, we get

x = 7 × 5 – 42 = 35 – 42 = – 7

x = 7 × 6 – 42 = 42 – 42 = 0

x = 7 × 7 – 42 = 49 – 42 = 7

Three years from now,

Aftab’s age = x + 3

Age of Aftab’s daughter = y + 3

According to the question,

(x + 3) = 3 (y + 3)

x + 3 = 3y + 9

x – 3y = 9 – 3

x – 3y = 6 … (ii)

x = 3y + 6

Putting, y = – 2, –1 and 0, we get

x = 3 × – 2 + 6 = – 6 + 6 =0

x = 3 × – 1 + 6 = – 3 + 6 = 3

x = 3 × 0 + 6 = 0 + 6 = 6

Algebraic representation

From equation (i) and (ii)

x – 7y = – 42 … (i)

x – 3y = 6 … (ii)

Graphical representation

2. The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.

Ans. Let cost of one bat be = Rs x

And, cost of one ball be = Rs y

3 bats and 6 balls are for Rs 3900

Therefore, 3x + 6y = 3900 … (i)

Dividing equation by 3, we get

x + 2y = 1300