Pair of Linear Equations in Two Variables
22 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 Solve the pair of equations 2x + 3y = 7 and x - y = 1 by the method of substitution. easy MCQ 1 mark Substitution method
- 2 Determine whether the pair of equations 5x - 2y = 7 and 10x - 4y = 20 are consistent, inconsistent, or represent the same straight line. Justify your answer. medium 3 marks Consistency of linear equations
- 3 A trader sells two types of nuts. Type A is sold at a profit of \rupee 8 per kg and Type B at a loss of \rupee 5 per kg. He sells a total of 50 kg of nuts and his overall profit is \rupee 140. How many kilograms of each type did he sell? hard 5 marks Solving word problems with profit and loss
- 4 For what value of k do the equations 3x + 4y = 12 and 6x + 8y = k represent the same straight line? medium MCQ 3 marks Condition for coincident lines
- 5 A small bakery makes two types of cakes. Plain cake gives a profit of \rupee 6 per cake and chocolate cake gives a loss of \rupee 4 per cake. If the bakery sells a total of 40 cakes in a day and the net profit is \rupee 80, how many plain and how many chocolate cakes were sold? easy 1 mark Forming equations from word problems
- 6 Solve the pair of equations 4x - 7y = 2 and 3x + 5y = -1 using the elimination method. medium 2 marks Elimination method for linear equations
- 7 For what value of k will the equations 5x - 3y = 12 and 10x - 6y = k represent the same straight line? easy MCQ 1 mark Condition for identical straight lines
- 8 Determine whether the pair of equations 3x + 2y = 7 and 6x + 4y = 20 are consistent, inconsistent, or represent the same straight line. Justify your answer. medium 2 marks Consistency of linear systems
- 9 Find the values of x and y that satisfy the equations 2x + 7y = 13 and 4x - 3y = 5 using Cramer's rule. hard 3 marks Cramer's rule
- 10 Find the zeroes of the quadratic polynomial x² - 5x + 6. medium MCQ Zeroes of Polynomial
- 11 What is the degree of a non-zero constant polynomial? medium MCQ Degree of Polynomial
- 12 Solve for x: 2x + 5 = 15. medium MCQ Linear Equations
- 13 Find the discriminant (D) of x² - 4x + 4 = 0. medium MCQ Quadratic Discriminant
- 14 If the roots of ax² + bx + c = 0 are real and equal, what is D? medium MCQ Nature of Roots
- 15 Expand (a + b)². medium MCQ Algebraic Identities
- 16 Factorise x² - 9. medium MCQ Difference of Two Squares
- 17 Solve pair of equations: x + y = 10 and x - y = 4. medium MCQ Pair of Linear Equations
- 18 What is the degree of a quadratic polynomial? medium MCQ Degree of Polynomial
- 19 If x = 2 is a root of x² - kx + 10 = 0, find k. medium MCQ Roots of Equation
- 20 What is the domain, range, or fundamental theorem introduced in 'Pair of Linear Equations in Two Variables' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 21 What is the derivative or integral formula associated with 'Pair of Linear Equations in Two Variables'? medium MCQ Calculus & Formulae
- 22 How do you find the solution set or optimum value in 'Pair of Linear Equations in Two Variables'? medium MCQ Problem Solving & Optimization