These AP 9th Class Maths Important Questions 6th Lesson Linear Equation in Two Variables will help students prepare well for the exams.

## AP State Syllabus 9th Class Maths 6th Lesson Important Questions and Answers Linear Equation in Two Variables

Question 1.

Express the following statement as a linear equation in two variables. “Neeraja and Girija of class IX students together contributed Rs. 300/- towards the C.M. relief fund”.

Solution:

Contribution of Neeraja = ₹x

Contribution of Girija = ₹y

Sum of contribution of Neeraja and Girija is 300/-

∴ x + y = 300.

Question 2.

Re state the following statement with appropriate conditions to make it true statement.

“For every real number x, x2 ≥ x”.

Solution:

If x ≤ 0 or x ≥ 1 then x^{2} ≥ x.

For every integer x, x^{2} ≥ x.

Question 3.

Write the statement given below as a linear equation two in variables. “The sum of two numbers x and y is 75”.

Solution:

The sum of two numbers x and y is 75.

∴ x + y = 75

Question 4.

If x = 2 – α and y = 2 + α in a solution of 5x + 3y – 7 = 0 and x = 2β + 1 and y = β – 1 in a solution of 3x – 2y + 6 = 0 then find the value of α + β.

Solution:

Given equation = 5x + 3y – 7 = 0

x = 2 – α and y = 2 + α

∴ 5(2 – α) + 3(2 + α) – 7 = 0

⇒ 10 – 5α+ 6 + 3α – 7 = 0

⇒ 9 – 2α = 0

⇒ 2α = 9 ⇒ α = \(\frac{9}{2}\) = 4.5

Given equation 3x – 2y + 6 = 0

x = 2β + 1 and y = β – 1

∴ 3(2β + 1)- 2(β – 1) + 6 = 0

⇒ 6β + 3 – 2β + 2 + 6 = 0

⇒ 4β + 11 = 0 ⇒ β = \(\frac{-11}{4}\)

∴ α + β = \(\frac{9}{2}\) – \(\frac{11}{4}\) = \(\frac{18-11}{4}\) = \(\frac{7}{4}\)

Question 5.

Draw the graph of the equation 2x + 3y = 6. Find the coordinates of the points where the graph cuts the coordinate axes.

Solution:

Given equation 2x + 3y = 6

Coordinates of the points are (3, 0) (0, 2)

Question 6.

Draw the graph of the linear equations 2x + 3y = 12. At what points, the graph of the equation cuts the X-axis and Y-axis.

Solution:

2x + 3y = 12

The graph of the equation cuts the x – axis = (6, 0)

y – axis = (0, 4)