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Linear Equations in Two Variables CBSE Class 9

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Linear Equations in Two Variables Topics

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Question 1/20

Q 1. The cost of a pen is three times more than twice the cost of a pencil. Represent this information as a linear equation in two variables. 

Solution

Let the cost of a pen be Rs. x and that of a pencil be Rs. y.

Then according to the given condition,

x = 2y + 3

x - 2y - 3 = 0 

Q 2. The number of boys in a school is 3 less than twice the number of girls. Represent this information as a linear equation in two variables. 

Solution

Let the number of boys be x and the number of girls be y.

Then according to the given condition,

x = 2y - 3

x - 2y + 3 = 0

Q 3. If the graph y = k is a straight line parallel to the x-axis, then k is 

Solution

The graph y = k is a straight line parallel to the x-axis, so k is a real number. 

Q 4. One of the numbers exceeds the other by 9. Write a linear equation in two variables to represent this statement.

Solution

Let

Bigger number = x

Smaller number = y

According to the condition, we get

x - y - 9 = 0

Q 5. If x = 2k - 1 and y = k is the solution of the equation 3x - 5y - 7 = 0, then find the value of k.

Solution

3x - 5y - 7 = 0

Putting x = 2k - 1 and y = k, 

3(2k - 1) - 5k - 7 = 0

6k - 3 - 5k - 7 = 0

k - 10 = 0

k = 10 

Q 6. Aaron is 5 years younger than Ron. Write a linear equation in two variables to represent this statement.

Solution

Let

Aaron’s age = x

Ron’s age = y

According to the condition, we get

x + 5 = y

x - y + 5 = 0

Q 7. The equations of two lines are given as 2x + 5 = 0 and 7y + 3 = 0. What is the angle between the two given lines? 

Solution

2x + 5 = 0 x =   and

7y + 3 = 0 y =

The graph x = k is a straight line parallel to the y-axis and the graph y = k is a straight line parallel to the x-axis, where k is a real number.

Both are perpendicular to each other.

Therefore, the angle between the two given lines is 90°.

Q 8. The graph x = k is a straight line parallel to the 

Solution

The graph x = k is a straight line parallel to the y-axis. 

Q 9. 6 erasers and 2 sharpeners cost Rs. 40. If the cost of one sharpener is Rs. 2, then what is the cost of one eraser? 

Solution

Let the cost of one eraser = Rs. x and the cost of one sharpener = Rs. y = Rs. 2

6x + 2y = 40

6x + 2 × 2 = 40

6x = 36

x = 6 

Q 10. Which of the following is the solution of 6x = y? 

Solution

Putting x = 2 and y = 12 in 6x = y,

6 × 2 = 12

12 = 12

LHS = RHS 

Q 11. The cost of a pen is four times the cost of a pencil. Write a linear equation in two variables to represent this statement. 

Solution

Let

The cost of a pen = x

The cost of a pencil = y

According to the condition, we get

x 4y = 0

Q 12. Any point which lies on the line is __________ to the equation. 

Solution

Any point which lies on the line is a solution to the equation.

Q 13. The equation of line x = −3 represents the line parallel to the 

Solution

The equation of line x = −3 represents the line parallel to the y-axis. 

Q 14. In 6 = −5y, what are the values of a, b and c?

Solution

6 = −5y

Subtracting 6 from both sides, we get

0 = 5y - 6

0x 5y 6 = 0

Here, a = 0, b = −5 and c = −6.

Q 15. The product of two numbers is 36. Represent this information as a linear equation in two variables. 

Solution

Let the two numbers be x and y.

xy = 36

Q 16. Every point on the ____ is of the form (x, 0). 

Solution

Every point on the x-axis is of the form (x, 0). 

Q 17. Every point (a, b) on the line AB gives a solution x = __ and y = __ of the equation. 

Solution

Every point (a, b) on the line AB gives a solution x = a and y = b of the equation. 

Q 18. Ram has some 5 rupee coins and some 10 rupee coins. The total amount possessed by him in all is Rs. 350. Represent this information as a linear equation in two variables. 

Solution

Let the number of 5 rupee coins be x and the number of 10 rupee coins be y.

So, the total amount will be given by

5x + 10 y which is Rs. 350

5x + 10y = 350

Q 19. Which of the following is the value of x in 2x + y = 2 if y = −2? 

Solution

Putting y = 2 in 2x + y = 2, we get

2x + y = 2

2x 2 = 2

x = 2

Q 20. Which of the following is not the solution of 2x - y = 6? 

Solution

Putting x = 0 and y = 6 in 2x - y = 6, we get

2 × 0 - 6 = 6

6 6

(0, 6) is not the solution of 2x - y = 6.

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