Class 9 Maths — Chapter 4: LINEAR EQUATIONS IN TWO VARIABLES
Chapter 4: LINEAR EQUATIONS IN TWO VARIABLES is a chapter in Class 9 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Definition and Standard Form of Linear Equations in Two Variables, Forming Linear Equations from Word Problems, Solution of a Linear Equation. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Definition and Standard Form of Linear Equations in Two VariablesCore conceptax + by + c = 0standard formtwo variablescoefficientsreal numbers
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▸Forming Linear Equations from Word Problemsword problemformulate equationrepresent statementmathematical modelapplication
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▸Solution of a Linear EquationCore conceptsolutionordered pair(x, y)satisfy the equationsubstitution
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▸Infinitely Many SolutionsCore conceptinfinitely many solutionsunique solutionmultiple solutionsnumber of solutions
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▸Finding Multiple SolutionsCore conceptfind solutionssubstitute valuesolve for variablex=0y=0
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▸Verifying Solutions and Finding UnknownsCore conceptverify solutioncheck solutionsubstitutefind kunknown constant
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▸Expressing One-Variable Equations in Two Variablesone variablezero coefficientax + 0y + c = 00x + by + c = 0express as
Chapter Summary
Understanding that a linear equation in two variables can be expressed in the standard form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. This includes identifying the values of a, b, and c from a given equation.
Translating a real-world situation or a verbal statement into a mathematical equation with two variables. For example, representing the relationship between the cost of a notebook and a pen as an equation.
Understanding that a solution to a linear equation in two variables is an ordered pair of values (x, y) that, when substituted into the equation, makes the statement true.
Recognizing the key property that a single linear equation in two variables has an infinite number of possible solutions, unlike a linear equation in one variable which has a unique solution.
Developing the skill to find several different solutions for a given linear equation. This is typically done by choosing an arbitrary value for one variable (e.g., x) and then solving the resulting one-variable equation for the other variable (y).
The ability to check if a given ordered pair (x, y) is a solution to an equation by substituting the values. This skill is also applied to find an unknown constant (e.g., 'k') in an equation when a specific solution is provided.
Understanding how a linear equation in one variable, like x = -5, can be written in the standard form of a two-variable equation by using a zero as the coefficient for the missing variable (e.g., 1x + 0y + 5 = 0).
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Show a real-world linear equation? Get Solution →
- Explain infinite solutions simply? Get Solution →
- Compare one-variable and two-variable equations? Get Solution →
- What is the general form of a linear equation in two variables? Get Solution →
- How many solutions does a linear equation in one variable, such as x + 1 = 0, have? Get Solution →
- According to the chapter summary, how many solutions does a linear equation in two variables have? Get Solution →
- Which of the following is an example of a linear equation in two variables mentioned in the text? Get Solution →
- In the equation 2x + 3y - 4.37 = 0, what is the value of 'c' when compared to the form ax + by + c = 0? Get Solution →
Did you know?
- 💡 The symbol 'x' for an unknown in algebra came from Arabic mathematicians.
- 💡 Ancient Egyptians solved equations over 3,500 years ago using a method called 'false position'.
- 💡 A straight line, which represents a linear equation, has infinitely many points.
- 💡 In computer programming, variables store information, just like 'x' and 'y' store numbers.
- 💡 The universe might be infinitely large, containing countless galaxies beyond our sight.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 7 key topics: Definition and Standard Form of Linear Equations in Two Variables, Forming Linear Equations from Word Problems, Solution of a Linear Equation, Infinitely Many Solutions, Finding Multiple Solutions, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 4: LINEAR EQUATIONS IN TWO VARIABLES important for board exams?
Class 9 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 9?
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