Linear Equation in Two Variables ⇒⇒ Exercise 4.1

Question 1

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

Solution :

Let the cost of a notebook be ₹x.

Let the cost of a pen be ₹y.

Since the cost of notebook is twice the cost of a pen.

Therefore, we can write the required linear equation in two variables to represent the above statement is given by

Cost of notebook = 2 × Cost of pen

x = 2y

To write it in the standard form of a linear equation in two variables (ax + by + c = 0), the equation is:

⇒ x - 2y = 0

Therefore, the required linear equation is x - 2y = 0.

Question 2 (i)

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 = 9.35

Solution :

Given , 2x + 3y = 9.35

To express this equation in the standard form ax + by + c =0, we simply move the constant term from the right side of the equation to the left side:

2x + 3y - 9.35 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 2

The coefficient of y is b = 3

The constant term is c = - 9.35

Question 2 (ii)

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

(ii) x - $ {y \over 5 }$ - 10 = 0

Solution :

Given , x - $ {y \over 5 }$ - 10 = 0

This equation is already in the standard form ax + by + c = 0.

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 1

The coefficient of y is b = - $ {1 \over 5 }$

The constant term is c = - 10

Question 2 (iii)

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

(iii) –2x + 3y = 6

Solution :

Given , –2x + 3y = 6

To express this equation in the standard form ax + by + c =0, we simply move the constant term from the right side of the equation to the left side:

–2x + 3y - 6 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = -2

The coefficient of y is b = 3

The constant term is c = - 6

Question 2 (iv)

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

(iv) x = 3y

Solution :

Given , x = 3y

To express this equation in the standard form ax + by + c =0, we simply move the term 3y from the right side of the equation to the left side:

x - 3y + 0 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 1

The coefficient of y is b = -3

The constant term is c = 0

Question 2 (v)

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

(v) 2x = –5y

Solution :

Given , 2x = –5y

To express this equation in the standard form ax + by + c =0, we simply move the term (–5y) from the right side of the equation to the left side:

2x + 5y + 0 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 2

The coefficient of y is b = 5

The constant term is c = 0

Question 2 (vi)

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

(vi) 3x + 2 = 0

Solution :

Given , 3x + 2 = 0

To express this equation in the standard form ax + by + c =0, we must include the y term. Since the original equation does not contain y, its coefficient must be zero:

3x + 0y + 2 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 3

The coefficient of y is b = 0

The constant term is c = 2

Question 2 (vii)

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

(vii) y – 2 = 0

Solution :

Given , y – 2 = 0

To express this equation in the standard form ax + by + c =0, we must include the x term. Since the original equation does not contain x, its coefficient must be zero:

0x + y – 2 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 0

The coefficient of y is b = 1

The constant term is c = -2

Question 2 (viii)

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

(viii) 5 = 2x

Solution :

Given , 5 = 2x

To express this equation in the standard form ax + by + c =0, we need to move all terms to one side and include the y term with a coefficient of zero.

2x + 0y – 5 = 0

Now , Comparing this equation with the standard form of the linear equation in two variables,

ax + by + c = 0, we get,

The coefficient of x is a = 2

The coefficient of y is b = 0

The constant term is c = -5