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Pair of Linear Equations in Two Variables - Solved Examples

Exercise 3.2

NCERT 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.


Solution

Let the present age of Aftab be x years and that of her daughter be y years.
Then, algebraic representation is given by the following equations :
Condition 1 - Seven years ago
$(x – 7) = 7(y – 7)$
$⇒ 7y – 49 = x – 7$
$⇒ x - 7y = - 42$

Condition 2 - Three years later
$(x + 3) = 3(y + 3)$
$⇒ x + 3 = 3y + 9$
$⇒ x – 3y = 6$

To obtain the equivalent graphical representation, let us find a few points on the line representing each equation.

For equation $ x - 7y = -42$ Pair of Linear Equations

For equation $ x - 3y = 6$ Pair of Linear Equations

We will plot both the equations on the graph.

Pair of Linear Equations



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


Solution

Let the cost of one bat be $x$ and the cost of one ball be $y$.
The cost of 3 bats and 6 balls is ₹ 3900.
The given conditions can be algebraically represented as:
$3x + 6y = 3900$ or
$x + 2y = 1300$

The cost of 1 bat and 3 balls is ₹ 1300.
The given conditions can be algebraically represented as:
$x + 3y = 1300$ or
To obtain the equivalent graphical representation, let us find a few points on the line representing each equation.

For equation $ x + 2y = 1300$ Pair of Linear Equations

For equation $ x + 3y = 1300$ Pair of Linear Equations

We will plot both the equations on the graph.

Pair of Linear Equations



3
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically.


Solution

Let the cost of 1 kg of apples be $x$ and the cost of 1 kg of grapes be $y$.
The cost of 2 kg of apples and 1 kg of grapes is ₹ 160.
The given conditions can be algebraically represented as:
$2x + 1y = 160$

The cost of 4 kg of apples and 2 kg of grapes is ₹ 300.
The given conditions can be algebraically represented as:
$4x + 2y = 300$ or
$2x + 1y = 150$ or

To obtain the equivalent graphical representation, let us find a few points on the line representing each equation.

For equation $ 2x + 1y = 160$ Pair of Linear Equations

For equation $ 2x + 1y = 150$ Pair of Linear Equations

We will plot both the equations on the graph.

Pair of Linear Equations