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Worksheet
Explore the methods to solve a pair of linear equations in two variables, including graphical, substitution, elimination, and cross-multiplication techniques.
Pair of Linear Equations in Two Variables - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Pair of Linear Equations in Two Variables from Mathematics for Class X (Mathematics).
Questions
Explain the graphical method of solving a pair of linear equations in two variables. What does the point of intersection represent?
Recall how to plot a line using its equation and interpret the intersection point.
Describe the substitution method for solving a pair of linear equations in two variables with an example.
Start by isolating one variable in one equation and then substitute it into the other equation.
How does the elimination method work in solving a pair of linear equations? Provide a step-by-step explanation.
Look for or create coefficients that are opposites for one variable to eliminate it.
What are the conditions for a pair of linear equations to have a unique solution, no solution, or infinitely many solutions?
Compare the ratios of the coefficients of x, y, and the constants in the two equations.
Solve the pair of equations 3x + 2y = 12 and 6x + 4y = 24 using the elimination method. What do you observe?
Notice that the second equation is a multiple of the first, suggesting they represent the same line.
A shopkeeper sells two types of pens. The cost of 5 pens of type A and 3 pens of type B is Rs. 79, while the cost of 2 pens of type A and 7 pens of type B is Rs. 89. Find the cost of each type of pen.
Use the elimination method to solve for one variable first.
Explain how to form a pair of linear equations from a word problem. Use the example of two numbers whose sum is 50 and difference is 10.
Define variables for the unknowns and translate the given conditions into equations.
What is the significance of the graphical representation of a pair of linear equations in understanding their solutions?
Consider how the position and slope of the lines affect their intersection.
Solve the pair of equations 0.4x + 0.3y = 1.7 and 0.7x - 0.2y = 0.8 using the substitution method.
Start by expressing y in terms of x from the first equation and then substitute into the second.
A fraction becomes 1/2 when 1 is subtracted from the numerator and 1 is added to the denominator. It becomes 1/3 when 1 is added to the numerator and 1 is subtracted from the denominator. Find the original fraction.
Set up equations based on the given conditions and solve the system.
Pair of Linear Equations in Two Variables - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Pair of Linear Equations in Two Variables to prepare for higher-weightage questions in Class X Mathematics.
Questions
Solve the pair of linear equations graphically: 2x + 3y = 8 and 4x + 6y = 7. What do you observe about their solutions?
Compare the ratios of the coefficients to determine the nature of the lines.
A fraction becomes 9/11 when 2 is added to both numerator and denominator. If 3 is added to both, it becomes 5/6. Find the fraction.
Set up equations based on the given conditions and solve them using substitution or elimination.
The sum of a two-digit number and the number obtained by reversing its digits is 66. If the digits differ by 2, find the number.
Express the numbers in terms of their digits and set up equations based on the given conditions.
Compare the graphical and algebraic methods of solving a pair of linear equations. Which method is more efficient and why?
Consider the accuracy and applicability of each method in different scenarios.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for seven days, while Susy paid ₹21 for five days. Find the fixed and additional charges.
Set up equations based on the total charges for different durations.
Explain the conditions under which a pair of linear equations has no solution, a unique solution, or infinitely many solutions.
Analyze the ratios of the coefficients of the equations.
The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and ball.
Use the elimination method to solve the system of equations.
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Set up equations based on the age conditions given.
A rectangular garden's length is 4m more than its width. Half the perimeter is 36m. Find the dimensions of the garden.
Express the perimeter in terms of the width and set up the equation.
The taxi charges in a city consist of a fixed charge plus a charge per km. For 10km, the charge is ₹105, and for 15km, it's ₹155. Find the fixed charge and the rate per km.
Set up linear equations based on the total charges for different distances.
Pair of Linear Equations in Two Variables - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Pair of Linear Equations in Two Variables in Class X.
Questions
Akhila went to a fair and spent ` 20 on rides and games. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs ` 3, and a game of Hoopla costs ` 4. Formulate the situation as a pair of linear equations and solve it graphically.
Consider expressing y in terms of x for the first equation and then substitute into the second equation for graphical representation.
Explain the conditions under which a pair of linear equations in two variables has no solution, a unique solution, or infinitely many solutions. Provide examples for each case.
Think about the graphical representation of each scenario to understand the conditions.
Champa purchased some pants and skirts. The number of skirts is two less than twice the number of pants. Also, the number of skirts is four less than four times the number of pants. Represent this situation algebraically and find the number of pants and skirts she bought.
Set up two equations based on the given conditions and solve them simultaneously.
The sum of a two-digit number and the number obtained by reversing its digits is 66. If the digits differ by 2, find the number. How many such numbers exist?
Express the two-digit number and its reverse in terms of x and y, then form equations based on the given conditions.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ` 27 for seven days, and Susy paid ` 21 for five days. Find the fixed charge and the charge for each extra day.
Set up equations based on the total charges for Saritha and Susy, considering the fixed and additional charges.
The ratio of incomes of two persons is 9:7, and the ratio of their expenditures is 4:3. If each saves ` 2000 per month, find their monthly incomes.
Express savings as income minus expenditure and set up proportional relationships.
A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both, it becomes 5/6. Find the fraction.
Cross-multiply to eliminate denominators and solve the resulting linear equations.
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Find their present ages.
Set up equations based on age relationships in the past and future.
The taxi charges in a city consist of a fixed charge plus a charge per km. For 10 km, the charge is ` 105, and for 15 km, it's ` 155. Find the fixed charge and the charge per km. What will be the charge for 25 km?
Set up linear equations based on the total charges for different distances.
A cricket team's coach buys 7 bats and 6 balls for ` 3800. Later, she buys 3 bats and 5 balls for ` 1750. Find the cost of each bat and ball.
Set up two equations based on the total costs for different purchases and solve them simultaneously.
Real Numbers encompass all rational and irrational numbers, forming a complete and continuous number line essential for various mathematical concepts.
Explore the world of Polynomials, understanding their types, degrees, and operations to solve algebraic expressions and equations effectively.
Explore the world of quadratic equations, learning to solve them using various methods like factoring, completing the square, and the quadratic formula.
A chapter that explores sequences where each term after the first is obtained by adding a constant difference, focusing on their properties, nth term, and sum formulas.
