Linear Equations in Two Variables quiz

Which of these is a linear equation in two variables?

The number of solutions of 3x + 2y = 6 is:

Which is a solution of x + 2y = 8?

In the equation 4x - 5y + 10 = 0, the value of b is:

The equation x = 4 written in two variables is:

If (1, k) is a solution of 3x + y = 7, then k is:

The point (0, 0) is a solution of:

Which pair satisfies y = 2x + 1?

The statement the sum of two numbers is 25 can be written as:

If x = 3 and y = -1 satisfy 2x + ky = 4, then k is:

Write two solutions of the equation 5x - y = 10. (2 marks)

Write the equation y - 3 = 0 in the form ax + by + c = 0 and state a, b and c. (2 marks)

Check whether (3, -2) is a solution of 2x + 3y = 0. (2 marks)

The cost of a pen is Rs 5 more than the cost of a pencil. Write a linear equation for this. (2 marks)

Find the value of k if (2, -3) is a solution of kx - y = 11. (2 marks)

Express y in terms of x for 3x + 4y = 12, and find y when x = 4. (2 marks)

Write a linear equation in two variables whose solutions include (1, 1) and (2, 2). (2 marks)

Why is x = 2 not considered an equation in only one variable on the Cartesian plane? (2 marks)

Find the point where the equation 2x + 5y = 10 meets the x-axis and the y-axis. (2 marks)

Give an example of a linear equation in two variables with c = 0 and write two of its solutions. (2 marks)

The perimeter of a rectangle is 40 cm. Taking length x and breadth y, write a linear equation. Find the breadth when the length is 12 cm, and give two more possible pairs of dimensions. (3 marks)

A shop sells apples at Rs 120 per kg and oranges at Rs 80 per kg. Ravi spends Rs 640. Write a linear equation and find three possible combinations in whole kilograms. (3 marks)

Find three solutions of 4x + 3y = 24 and check one of them by substitution. (3 marks)

The work done by a body is directly proportional to the distance travelled, with a constant force of 5 units. Write the equation W = 5d. Find W when d = 3 units and d when W = 40 units. (3 marks)

The sum of the ages of a father and son is 48 years. Write a linear equation. If the son is 14 years old, find the father's age. If the father is three times as old as his son, find both ages. (3 marks)

Read the passage and answer the questions. A school sells tickets for a play at Rs 100 for adults and Rs 50 for children. On the first day, it collected Rs 5,000. (i) Write a linear equation in two variables for this. (ii) If 30 adult tickets were sold, how many children's tickets were sold? (iii) Give two other possible pairs. (5 marks)

Read the passage and answer the questions. A mobile company charges a fixed rent of Rs 200 per month plus Rs 2 per minute of calls. (i) Write an equation for the total bill y when x minutes are used. (ii) Find the bill for 150 minutes. (iii) How many minutes were used if the bill is Rs 560? (5 marks)

Read the passage and answer the questions. In a cricket match, Rohit and Virat together scored 176 runs. (i) Write a linear equation for this. (ii) If Virat scored 82 runs, find Rohit's score. (iii) If Rohit scored 20 runs more than Virat, find their scores. (5 marks)

Read the passage and answer the questions. A shopkeeper mixes two types of rice costing Rs 60 per kg and Rs 40 per kg to get a mixture worth Rs 1,000. (i) Write a linear equation in two variables. (ii) If he uses 10 kg of the first type, how much of the second does he use? (iii) Write one more solution with whole numbers. (5 marks)

Read the passage and answer the questions. Temperatures in Celsius C and Fahrenheit F are related by F = (9/5)C + 32. A doctor's thermometer shows 98.6 degrees F. (i) Find the temperature in Celsius. (ii) What is the boiling point of water in Fahrenheit? (iii) Is the relation a linear equation in two variables? Explain. (5 marks)

Make a table of five solutions of 2x + y = 8 and plot them on the Cartesian plane. Explain why all solutions lie on one straight line. (6 marks)

Write the linear equations for the following: (i) the sum of two numbers is 12 (ii) one number is three times another (iii) a number exceeds another by 4. Find two solutions of each and plot the solutions of (i). (6 marks)

A taxi charges Rs 30 for the first km and Rs 15 for every subsequent km. Write a linear equation, make a table of fares for 1 to 5 km, and plot the points. (6 marks)

Plot the solutions (0, 3), (1, 2), (2, 1) and (3, 0) and find the linear equation they satisfy. Check whether (4, -1) also satisfies it. (6 marks)

Explain with examples the difference between a linear equation in one variable and in two variables. Show how 2x + 4 = 0 can be written in two variables and plot three of its solutions. (6 marks)