Question

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Answer 1

Answer:

A pair of linear equations in two variables, which has a solution, is called a consistent pair of linear equations. A pair of linear equations which are equivalent has infinitely many distinct common solutions. Such a pair is called a dependent pair of linear equations in two variables.Solutions:Let the present age of Aftab be ‘x’.

And, the present age of his daughter be ‘y’.

Now, we can write, seven years ago,

Age of Aftab = x-7

Age of his daughter = y-7

According to the question,

x−7 = 7(y−7)

⇒x−7 = 7y−49

⇒x−7y = −42 ………………………(i)

Also, three years from now or after three years,

Age of Aftab will become = x+3.

Age of his daughter will become = y+3

According to the situation given,

x+3 = 3(y+3)

⇒x+3 = 3y+9

⇒x−3y = 6 …………..…………………(ii)

Subtracting equation (i) from equation (ii) we have

(x−3y)−(x−7y) = 6−(−42)

⇒−3y+7y = 6+42

⇒4y = 48

⇒y = 12

The algebraic equation is represented by

x−7y = −42

x−3y = 6

For, x−7y = −42 or x = −42+7y

The solution table is

Ncert solutions class 10 chapter 3-1

For, x−3y = 6 or x = 6+3y

The solution table is

Ncert solutions class 10 chapter 3-2

The graphical representation is:

Ncert solutions class 10 chapter 3-3

Answer 2

Answer:

1) consistent

2) 17

3) unique solution

4) intersect only at point

5) 3

6) unique solution

7) (8,0)

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