Linear Polynomial in Two Variables Class 9 Maths | Introduction to Linear Polynomials

Understand it

A solution of a linear equation in two variables is an ordered pair (x, y) that makes the equation true. Unlike a one-variable linear equation, a two-variable linear equation usually has many solutions, and these solutions form a straight line on a graph.

Example

For x + y = 6, the ordered pairs (1, 5), (2, 4), and (6, 0) are solutions because each pair has x + y equal to 6.

Formula and rule

Standard form: ax + by + c = 0.

A solution is an ordered pair (x, y) satisfying the equation.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Check whether (4, -1) satisfies x - 2y = 6.

1Substitute x = 4 and y = -1: 4 - 2(-1) = 4 + 2 = 6.
2So it is a solution.

Method you can reuse

Take the ordered pair, substitute the first value for x and the second for y, simplify both sides, and conclude whether the equation is satisfied.

Visual tip

A two-column table of x and y values can be used before plotting points on the coordinate plane.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Is (3, 2) a solution of 2x + y = 8?

Think first, then show answer

Yes, (3, 2) is a solution because 2(3) + 2 = 6 + 2 = 8, which satisfies the equation.

Common wrong answer

For (2, 5), students may substitute x = 5 and y = 2 by reversing the order, leading to a wrong conclusion.

Don't mix this up

Students sometimes write only one number as the answer. In two variables, the answer must be an ordered pair like (2, 4).

Exam tip

Substitute x and y in the correct order. The first coordinate is x and the second coordinate is y.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be asked to verify an ordered pair, complete a value table, or generate two solutions for an equation.

1
Enough for 1 mark
A linear polynomial or linear equation in two variables has the form ax + by + c = 0, where x and y are variables, a, b, and c are constants, and a and b are not both zero.
2
Add for 2 marks
Example: For x + y = 6, the ordered pairs (1, 5), (2, 4), and (6, 0) are solutions because each pair has x + y equal to 6.
3
Add for 3 marks
A solution of a linear equation in two variables is an ordered pair (x, y) that makes the equation true.

Use the concept graph around this idea instead of revising it in isolation.

Graphical Visualisation of Linear Polynomials

Graphical visualisation means representing the solutions of a linear equation in two variables as points on the Cartesian plane. These points lie on a straight line.

Solving Linear Polynomials

Solving linear polynomials means finding the value or values of variables that make the given linear equation true. At this level, substitution, simple elimination, and verification are useful methods.

Polynomial — Definition and Degree

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.

Linear Polynomial in One Variable

A linear polynomial in one variable is a polynomial of degree 1, usually written as ax + b, where a and b are constants and a is not equal to 0.

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Linear Polynomial in Two Variables

Understand it

See it worked out

Check yourself

Linear Polynomial in Two Variables diagram

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Linear Polynomial in Two Variables

Understand it

See it worked out

Check yourself

Linear Polynomial in Two Variables diagram

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page