NCERT Solutions for class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables

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NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables are provided in this article. A pair of linear equations in two variables having a solution is known as a consistent pair of linear equations. Equivalent pair of linear equations has infinitely many distinct common solutions, such a pair of solutions is known as a dependent pair of linear equations in two variables.

Class 10 Maths Chapter 3 Linear Equations in Two Variables belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 10 Maths Examination. The NCERT solutions of the chapter include questions related to the Substitution method, Elimination method, and Cross-multiplication method.

Download PDF: NCERT Solutions for Class 10 Mathematics Chapter 3

NCERT Solutions for Class 10 Mathematics Chapter 3

NCERT Solutions

Important Topics in Class 10 Maths Chapter 3

Linear Equations are the equations in which the powers of all the involved variables are one.

The general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be simultaneously zero.

The solution of a linear equation in two variables is generally a pair of values, one for x and the other for y, which makes the two sides of the equation equal.

For example: If 3x + y = 6, then (0,6) is one of its solutions as it satisfies the equation.

Graph of Linear Equation in two variables: A linear equation in two variables can be geometrically represented as a straight line.

A pair of linear equations in two variables can be represented as shown below –

\(a_1x + b_1y+c_1=0\\ a_2x + b_2y+c_2=0\)

The solution for a consistent pair of linear equations can be found using various methods.

i) Elimination method

ii) Substitution Method

iii) Cross-multiplication of solving linear equations

iv) Graphical method

NCERT Solutions For Class 10 Maths Chapter 3 Exercises:

The detailed solutions for all the NCERT Solutions for Pair of Linear Equations in Two Variables under different exercises are as follows:

Related Topics:

Difference between linear and non-linear equations	Pair of Linear Equations in Two Variables Important Questions	Pair of Linear Equations in Two Variables Formula

CBSE Class 10 Mathematics Study Guides:

Geometry	Math Formula	Maths Study Material
NCERT Solutions for Class 10 Maths	Class 10 Maths Notes	Mensuration
Difference between in Maths	Calculus	Math MCQs

CBSE X Related Questions

1.
A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))
- \(314 \sqrt{2}\) \(\text{cm}^{2}\)
- \(314\) \(\text{cm}^{2}\)
- \(\frac{3140}{3}\) \(\text{cm}^{2}\)
- \(3140 \sqrt{2}\) \(\text{cm}^{2}\)
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2.
Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)
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3.
For any natural number n, \( 5^n \) ends with the digit :
- 0
- 5
- 3
- 2
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4.
The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :
- 0
- 1
- 3
- 2
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5.
If \(PQ\) and \(PR\) are tangents to the circle with centre \(O\) and radius \(4 \text{ cm}\) such that \(\angle QPR = 90^{\circ}\), then the length \(OP\) is
- \(4 \text{ cm}\)
- \(4\sqrt{2} \text{ cm}\)
- \(8 \text{ cm}\)
- \(2\sqrt{2} \text{ cm}\)
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6.
Solve the linear equations \(3x + y = 14\) and \(y = 2\) graphically.
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