Solving Linear Polynomials Class 9 Maths | Introduction to Linear Polynomials

Understand it

For one variable, solving usually means isolating the variable. For two variables, one equation can have many solutions, while two linear equations may be solved together by substitution or elimination. Verification is important because it catches sign and arithmetic mistakes.

Example

To solve x + y = 9 and x - y = 1, add the equations to get 2x = 10, so x = 5. Then 5 + y = 9 gives y = 4.

Formula and rule

Elimination idea: add or subtract equations so that one variable cancels.

Substitution idea: express one variable in terms of the other and replace it in the second equation.

See it worked out

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

Worked example

Solve 2x + y = 11 and x + y = 7.

1Subtract the second equation from the first: x = 4.
2Put x = 4 in x + y = 7, so y = 3.
3Solution is (4, 3).

Method you can reuse

Align equations, decide whether addition or subtraction cancels a variable, solve for one variable, substitute back to find the other, and verify both original equations.

Visual tip

A simple flow chart can show: choose method, remove one variable, find first value, find second value, verify.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Solve x + y = 7 and x - y = 3 using elimination.

Think first, then show answer

Adding the equations gives 2x = 10, so x = 5. Substituting in x + y = 7 gives y = 2, so the solution is (5, 2).

Common wrong answer

For x + y = 7 and x - y = 3, a wrong answer is y = 5 if the student adds y and -y as 2y instead of 0.

Don't mix this up

Students often eliminate the wrong terms or forget to change signs when subtracting equations.

Exam tip

After solving, substitute the values in the original equation or equations, not only in your last working line.

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 solve a pair, verify a claimed solution, or identify an error in a student's elimination step.

1
Enough for 1 mark
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.
2
Add for 2 marks
Example: To solve x + y = 9 and x - y = 1, add the equations to get 2x = 10, so x = 5. Then 5 + y = 9 gives y = 4.
3
Add for 3 marks
For one variable, solving usually means isolating the variable.

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

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.

Linear Polynomial in Two Variables

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.

Intersection of Two Linear Polynomials

The intersection of two linear graphs is the point where the two lines meet. Algebraically, it represents the common solution of the two linear equations.

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.

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Solving Linear Polynomials

Understand it

See it worked out

Check yourself

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Solving Linear Polynomials

Understand it

See it worked out

Check yourself

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page