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Chapter 13: Linear Equation in Two Variables Exercise – 13.1

Question: 1

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

(i) - 2x + 3y = 12

(ii) x - y/2 - 5 = 0

(iii) 2x + 3y = 9.35

(iv) 3x = -7y

(v) 2x + 3 = 0

(vi) y - 5 = 0

(vii) 4 = 3x

(viii) y = x/2 ;

Solution:

(i) We are given

- 2x + 3y = 12

- 2x + 3y - 12 = 0

Comparing the given equation with ax + by + c = O

We get, a = - 2; b = 3; c = -12

(ii) We are given

x - y/2 - 5= 0

Comparing the given equation with ax + by + c = 0,

We get, a = 1; b = – 1/2, c = – 5

(iii) We are given

2x + 3y = 9.35

2x + 3y - 9.35 =0

Comparing the given equation with ax + by + c = 0

We get, a = 2; b = 3; c = - 9.35

(iv) We are given

3x = - 7y

3x + 7y = 0

Comparing the given equation with ax+ by + c = 0,

We get, a = 3; b = 7; c = 0

(v) We are given

2x + 3 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 2; b = 0; c = 3

(vi) We are given

y - 5 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 0; b = 1; c = – 5

(vii) We are given

4 = 3x

3x - 4 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 3; b = 0; c = - 4

(viii) We are given

y = x/2

Taking L.C.M ⟹ x - 2y = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 1; b = – 2; c = 0

 

Question: 2

Write each of the following as an equation in two variables:

(i) 2x = – 3

(ii) y = 3 

(iii) 5x = 7/ 2

(iv) y = 3/2x

Solution:

(i) We are given,

2x = - 3

Now, in two variable forms the given equation will be

2x + 0y + 3 = 0

(ii) We are given,

y = 3

Now, in two variable forms the given equation will be

0 x + y - 3 = 0

(iii) We are given,

5x = – 7/2

Now, in two variable forms the given equation will be

5x + 0y + 7/2 = 0

10x + 0y - 7 = 0

(iv) We are given,

y =  32x  (Taking L.C.M on both sides)

Now, in two variable forms the given equation will be

3x - 2y + 0 = 0

 

Question: 3

The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Solution:

Let the cost of fountain pen be y and cost of ball pen be x.

According to the given equation, we have

x = y/2 − 5

⟹ 2x = y - 10

⟹ 2x - y + 10 = 0

Here y is the cost of one fountain pen and x is that of one ball pen.


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