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Chapter Analysis
Intermediate6 pages • EnglishQuick Summary
This chapter on linear equations in two variables introduces students to equations of the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero. It explores the concept of solutions to these equations, which are ordered pairs (x, y) that satisfy the equation. The chapter describes how there are infinitely many solutions to such equations and includes examples of how to find these solutions. The understanding of graphing these equations on the Cartesian plane is also highlighted.
Key Topics
- •Linear equations in two variables
- •Solutions of linear equations
- •Graphical representation of linear equations
- •Formulating equations from real-world scenarios
- •Infinite solutions concept
- •Cartesian plane graphing
Learning Objectives
- ✓Understand the form of linear equations in two variables
- ✓Identify and demonstrate multiple solutions for a given equation
- ✓Graph linear equations on the Cartesian plane
- ✓Formulate linear equations from given real-life situations
- ✓Explain why linear equations in two variables have infinite solutions
Questions in Chapter
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Page 57
Which one of the following options is true, and why? y = 3x + 5 has (i) a unique solution, (ii) only two solutions, (iii) infinitely many solutions
Page 58
Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Page 59
Additional Practice Questions
Write a linear equation in two variables using the following information: The sum of two numbers is 50.
easyAnswer: Let the two numbers be x and y. The linear equation is x + y = 50.
Determine the solution for the equation 4x + 5y = 20 when x = 0.
mediumAnswer: Substituting x = 0 in the equation gives 5y = 20. Solving this, y = 4. Thus, the solution is (0, 4).
If the line equation is 3x + 4y = 12, find one solution where both x and y are integers.
mediumAnswer: By trying different values, one solution is x = 0, y = 3, which satisfies the equation: 3(0) + 4(3) = 12.
Explain why the equation x + y = 1 does not have a unique solution.
easyAnswer: The equation x + y = 1 represents a line in the Cartesian plane, and every point on this line is a solution, thus having infinitely many solutions.
Graph the equation 2x - 3y = 6. What is one visible solution on the graph?
hardAnswer: Plotting the points that satisfy the equation, one visible solution is (3, 0), where when x = 3, y = 0 satisfies the equation.