AP State Syllabus AP Board 9th Class Maths Solutions Chapter 6 Linear Equation in Two Variables Ex 6.1 Textbook Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 6th Lesson Linear Equation in Two Variables Exercise 6.1

Question 1.

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

i) 8x + 5y – 3 = 0

Solution:

8x + 5y – 3 = 0

⇒ 8x + 5y + (- 3) = 0

Here a = 8, b = 5 and c = – 3

ii) 28x – 35y = – 7

Solution:

28x – 35y = – 7

⇒ 28x + (- 35) y + 7 = 0

Here a = 28, b = – 35 and c = 7

iii) 93x = 12- 15y

Solution:

93x = 12 – 15y

⇒ 93x + 15y -12 = 0

⇒ 93x + 15y + (- 12) = 0

Here a = 93, b = 15 and c = – 12

iv) 2x = – 5y

Solution:

2x = – 5y

⇒ 2x + 5y = 0

Here a = 2, b = 5 and c = 0

v) \(\frac{x}{3}+\frac{y}{4}=7\)

Solution:

\(\frac{x}{3}+\frac{y}{4}=7\)

⇒ \(\frac{x}{3}+\frac{y}{4}-7=0\)

⇒\(\frac{4 x+3 y-84}{12}=0\)

⇒ 4x + 3y – 84 = 0

Here a = 4, b = 3 and c = – 84

vi) y = \(-\frac{3}{2} x\)

Solution:

y = \(-\frac{3}{2} x\)

⇒ 2y = -3x

⇒ 3x + 2y = 0

Here a = 3, b = 2 and c = 0

vii) 3x + 5y = 12

Solution:

3x + 5y = 12

⇒ 3x + 5y + (- 12) = 0

Here a = 3, b = 5 and c = – 12

Question 2.

Write each of the following in the form of ax + by + c = 0 and find the values of a, b and c.

i) 2x = 5

Solution:

2x – 5 = 0

a = 2

b = 0

c = -5

ii) y – 2 = 0

Solution:

y – 2 = 0

a = 0

b = 1

c = – 2

iii) \(\frac{y}{7}\) = 3

Solution:

\(\frac{y}{7}\) = 3

y = 21

y – 21 = 0

a = 0

b = 1

c = -21

iv) x = \(-\frac{14}{13}\)

x = \(-\frac{14}{3}\)

⇒ 13x = – 14

⇒ 13x + 14 = 0

a = 13

b = 0

c = 14

Question 3.

Express the following statements as a linear equation in two variables,

i)The sum of two numbers is 34.

Solution:

x + y = 34; x, y are any two numbers ⇒ x + y – 34 = 0

ii) The cost of a ball pen is ?5 less than half the cost of a fountain pen.

Solution:

Let the cost of a fountain pen = x

Let the cost of ball pen = y

Then y = x – 5 or x – y – 5 = 0

iii) Bhargavi got 10 more marks than double of the marks of Sindhu. |l M)

Solution:

Let Sindhu’s marks = x

Bhargavi’s marks = y

Then by problem y = 2x + 10 or 2x – y + 10 = 0

iv) The cost of a pencil is ₹2 and one ball point pen costs ₹15. Sheela pays ₹100 for the pencils and pens she purchased.

Solution:

Giver: that cost of a pencil = ₹2

Cost of a ball point pen = ₹15

Let the number of pencils purchased = x

Let the number of pens purchased = y

Then the total cost of x – pencils = 2x

Then the total cost of y – pens = 15y

By problem 2x + 15y = 100