Gujarat Board GSEB Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 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 and the cost of a pen be ₹ y.

Then according to the problem

x = 2y

⇒ x – 2y = 0

which is the required equation in two variables x and y.

Question 2.

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

(ii) x – \(\frac {y}{5}\) – 10 = 0

(iii) -2x + 3y = 6

(iv) x = 3y

(v) 2x = -5y

(vi) 3x + 2 = 0

(vii) y – 2 = 0

(uiii) 5 = 2x

Solution:

(i) 2x + 3y = \(9 . \overline{35}\)

2x + 3y – \(9 . \overline{35}\) = 0

Comparing with the standard form of the equation, ax + by + c = 0, we get

a = 2, b = 3, c = – \(9 . \overline{35}\)

(ii) x – y – 10 = 0

1x + \(\left(\frac{-1}{5}\right)\)y + (-10) = 0

Comparing with the standard form of equation ax + by + c = 0, we get

a = 1, b = \(\left(\frac{-1}{5}\right)\), c = -10

(iii) -2x -3y = 6

(-2)x + 3y -6 = 0

(-2)x + 3y + (-6) = 0

Comparing with the standard form of equation ax + by + c = 0, we get

a = -2, b = 3, c = -6

(iv) x = 3y

x – 3y = 0

⇒ 1x + (-3)y + 0 = 0

Comparing with the standard form of equation

ax + by + c = 0, we get

a = 1, b = -3, c = 0

(v) 2x = -5y

2x + 5y + 0 = 0

Comparing with the standard form of equation

i.e., ax + by + c = 0, weget

a = 2, b = 5, c = 0

(vi) 3x + 2 = 0

3x + (0)y + 2 = 0

Comparing with the standard form of equation

ax + by + c = 0, we get

a = 3, b = 0, c = 2

y – 2 = 0

0x + ly + (-2) = 0

Comparing with the standard form of equation

ax + by + e = 0, we get

a = 3, b = 0, c = 2

(vii) y – 2 = 0

= 0x + ly + (-2) = 0

Comparing with the standard form of equation

ax + by + c = 0, we get

a = O, b = 1, c = -2

(viii) 5 = 2x

= -2x + 5 = 0

(-)x + (0)y + 5 = 0

Comparing with the standard form of equation

ax + by + c = 0, we get

a = -2, b = 0, c = 5