Pair of Linear Equations in Two Variables quiz

The pair of equations x + 2y = 3 and 2x + 4y = 6 has:

If a pair of linear equations is inconsistent, the lines representing them are:

The solution of x + y = 5 and x - y = 1 is:

For what value of k does the pair x + 2y = 5 and 3x + ky = 15 have infinitely many solutions?

The pair 2x + 3y = 9 and 4x + 6y = 18 represents lines which are:

The pair of equations 3x - 5y = 4 and 9x - 15y = 11 has:

If x = a and y = b is the solution of x - y = 2 and x + y = 4, then a and b are:

The value of k for which the pair kx + 3y = k - 3 and 12x + ky = k has no solution is:

The graph of the equation y = 3 is a line:

A pair of linear equations which has a unique solution x = 2, y = -3 is:

On comparing the ratios a1/a2, b1/b2 and c1/c2, find whether the lines 5x - 4y + 8 = 0 and 7x + 6y - 9 = 0 intersect at a point, are parallel or coincide. (2 marks)

Check whether the pair 3x + 2y = 5 and 2x - 3y = 7 is consistent or inconsistent. (2 marks)

Romila buys 2 pencils and 3 erasers for Rs 9. Her friend Sonali buys 4 pencils and 6 erasers of the same kind for Rs 18. Represent this algebraically and state the number of possible solutions. (2 marks)

2 kg of apples and 1 kg of grapes cost Rs 160 on a day. After a month, 4 kg of apples and 2 kg of grapes cost Rs 300. Represent the situation algebraically and explain why it has no solution if prices are assumed unchanged. (2 marks)

The difference between two numbers is 26 and one number is three times the other. Find them. (2 marks)

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. (2 marks)

Solve 0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3 by the elimination method. (2 marks)

Akhila goes to a fair where a ride on the Giant Wheel costs Rs 3 and a game of Hoopla costs Rs 4. She plays Hoopla half as many times as she rides the Giant Wheel and spends Rs 20. Find the number of rides and games. (2 marks)

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the pair formed has parallel lines as its graphical representation. (2 marks)

Find the value of k for which the pair 3x + y = 1 and (2k - 1)x + (k - 1)y = 2k + 1 has no solution. (2 marks)

The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball. (3 marks)

The taxi charges in a city consist of a fixed charge together with a charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. Find the fixed charge, the charge per km, and the amount to be paid for travelling 25 km. (3 marks)

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for a book kept for five days. Find the fixed charge and the charge for each extra day. (3 marks)

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. (3 marks)

A motorboat goes 30 km downstream in 2 hours and 18 km upstream in 2 hours. Taking the speed of the boat in still water as u km/h and the speed of the stream as v km/h, form a pair of linear equations and find u and v. (3 marks)

Read the passage and answer the questions. A school canteen sells sandwiches and juice packs. On Monday, Rahul bought 2 sandwiches and 3 juice packs for Rs 130. On Tuesday, Neha bought 3 sandwiches and 2 juice packs for Rs 145. (i) Form the pair of linear equations, taking the cost of a sandwich as Rs x and of a juice pack as Rs y. (ii) Find the cost of one sandwich and one juice pack. (iii) How much would 5 sandwiches and 5 juice packs cost? Can this be found without solving fully? Explain. (5 marks)

Read the passage and answer the questions. A mobile company offers two plans. Plan A charges a fixed Rs 100 per month plus Rs 2 per GB of extra data. Plan B charges a fixed Rs 160 per month plus Rs 1 per GB of extra data. (i) Write the monthly cost y for x GB of extra data under each plan. (ii) For how many GB of extra data do the two plans cost the same, and what is that cost? (iii) Which plan should a customer choose who uses 80 GB of extra data per month? Explain. (5 marks)

Read the passage and answer the questions. The perimeter of a rectangular playground is 100 m and its length is 10 m more than its breadth. The school wants to fence it and lay grass inside. (i) Form the pair of equations for length l and breadth b. (ii) Find the length and breadth. (iii) Find the area of grass required. (5 marks)

Read the passage and answer the questions. In a zoo, there are some peacocks and some deer. A zookeeper counts 80 heads and 200 legs in total. (i) Form a pair of linear equations, taking x peacocks and y deer. (ii) Find the number of peacocks and deer. (iii) What would the zookeeper conclude if he counted 80 heads but 330 legs? Explain. (5 marks)

Read the passage and answer the questions. In a cyclic quadrilateral ABCD, opposite angles are supplementary. The angles are A = 4y + 20, B = 3y - 5, C = -4x and D = -7x + 5, all in degrees. (i) Write two equations using the property of opposite angles of a cyclic quadrilateral. (ii) Solve them to find x and y. (iii) Find the four angles of the quadrilateral. (5 marks)

Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. Find the area of the triangle. (6 marks)

Solve the following pairs graphically and state whether each is consistent, inconsistent or dependent: (i) x + y = 5 and 2x + 2y = 10 (ii) x - y = 8 and 3x - 3y = 16 (iii) 2x + y - 6 = 0 and 4x - 2y - 4 = 0. Draw the graphs on separate axes. (6 marks)

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Form a pair of linear equations, solve it by the elimination method, and verify the answer. Explain the general form 10x + y used for a two-digit number. (6 marks)

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Form the pair of equations, solve it by substitution, and draw the graph of the two equations to show the solution. (6 marks)

Explain, with one example of each, how the ratios a1/a2, b1/b2 and c1/c2 decide whether a pair of linear equations has a unique solution, no solution or infinitely many solutions. Draw a rough graph for each example and describe a real-life situation that leads to an inconsistent pair. (6 marks)