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Chapter Analysis
Intermediate17 pages • EnglishQuick Summary
Chapter 3 of the Class 10 Math textbook focuses on pairs of linear equations in two variables. It explores different methods of solving these equations, such as graphical, substitution, and elimination methods. The chapter also discusses the types of solutions these equations can have: unique, none, or infinite, which depend on the relationships between the lines they represent. Real-life examples and practice exercises help in understanding the application of these concepts in everyday situations【4:0†class-10-math-chapter-3.pdf】.
Key Topics
- •Graphical Method of Solving Linear Equations
- •Substitution Method
- •Elimination Method
- •Conditions for Consistency
- •Applications of Linear Equations
- •Dependent and Independent Equations
- •Real-life Situations Modeled by Linear Equations
Learning Objectives
- ✓Understand and solve pairs of linear equations graphically.
- ✓Apply the substitution method to solve linear equations.
- ✓Use the elimination method to find solutions for pairs of linear equations.
- ✓Determine the consistency of linear equation pairs.
- ✓Model real-world problems using linear equations.
- ✓Distinguish between dependent, independent, and inconsistent pairs of equations.
Questions in Chapter
Solve the following pair of linear equations by the elimination method and the substitution method: (i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2
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Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
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Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
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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.
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Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
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A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
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Additional Practice Questions
Consider a two-digit number where the digit sum equals 8. When the digits are reversed, the new number is 36 more than the original number. What is the number?
mediumAnswer: Let the tens digit be x and the units digit be y. Then the number is 10x + y. According to the conditions: x + y = 8 and 10y + x = 10x + y + 36. Solving gives the number as 35.
Two angles are supplementary. The larger angle is twice the smaller. Find the angles.
easyAnswer: Let the angles be x and y, where x + y = 180 and y = 2x. Solving gives x = 60 and y = 120.
John has a collection of 100 coins consisting of only 5-cent and 10-cent coins. If the total value is $7.00, how many coins of each type does he have?
hardAnswer: Let x be the number of 5-cent coins and y the number of 10-cent coins. Then 0.05x + 0.10y = 7.00 and x + y = 100. Solving gives 40 coins of 5-cents and 60 coins of 10-cents.
In a class of 35 students, the number of girls is 6 more than twice the number of boys. Find how many boys and girls are in the class.
mediumAnswer: Let the number of boys be x and girls be y. Then x + y = 35 and y = 2x + 6. Solving gives x = 11 boys and y = 24 girls.
A garden's length is twice its width. If the perimeter is 60 meters, what are the dimensions?
easyAnswer: Let the width be x and length be 2x. Then 2(x + 2x) = 60. Solving gives dimensions as 10 m (width) and 20 m (length).