Intersection of Two Linear Polynomials Class 9 Maths | Introduction to Linear Polynomials

Understand it

When two straight lines meet at one point, the coordinates of that point satisfy both equations. Solving the pair of equations gives the same ordered pair as the intersection point on the graph. This connects algebraic solving with graphical meaning.

Example

The lines x + y = 6 and x - y = 2 intersect at (4, 2) because 4 + 2 = 6 and 4 - 2 = 2.

Formula and rule

Common solution rule: if (x, y) lies on both lines, it satisfies both linear equations.

See it worked out

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

Worked example

Solve x + y = 9 and x - y = 1.

1Adding gives 2x = 10, so x = 5.
2Then y = 4.
3Graphically, the two lines intersect at (5, 4).

Method you can reuse

Draw or solve both equations, find the common ordered pair, check it in both equations, and state it as the intersection point.

Sketch it in your answer

Draw both straight lines on the same coordinate plane and mark the crossing point with its ordered-pair coordinates.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What does the intersection point of x + y = 8 and x - y = 2 represent?

Think first, then show answer

It represents the ordered pair that satisfies both equations at the same time; solving gives (5, 3).

Common wrong answer

A student may write only x = 5 for the intersection, but a point on a plane needs both x and y coordinates.

Don't mix this up

Students sometimes read the crossing point from the graph but forget to write it as an ordered pair.

Exam tip

Always verify the intersection point in both equations, especially if the graph scale is small.

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 find the point of intersection algebraically, identify it from a graph, or explain its meaning as a common solution.

1
Enough for 1 mark
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.
2
Add for 2 marks
Example: The lines x + y = 6 and x - y = 2 intersect at (4, 2) because 4 + 2 = 6 and 4 - 2 = 2.
3
Add for 3 marks
When two straight lines meet at one point, the coordinates of that point satisfy both equations.

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

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.

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.

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.

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.

Previous: Special Cases — Horizontal and Vertical Lines Back to full mind map

Intersection of Two Linear Polynomials

Understand it

See it worked out

Check yourself

Intersection of Two Linear Polynomials diagram

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Intersection of Two Linear Polynomials

Understand it

See it worked out

Check yourself

Intersection of Two Linear Polynomials diagram

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page