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.
Practice This ConceptMain explanation
Teacher explanation
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.
Simple analogy
Ordered pair means order matters: x first, y second.
Common confusion
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.
Study the linear polynomial in two variables diagram carefully
Use the labelled diagram to keep linear polynomial in two variables clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of linear polynomial in two variables in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on linear polynomial in two variables.
Revision cue
Revise linear polynomial in two variables through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of linear polynomial in two variables in one clean line.
2-mark use
Define linear polynomial in two variables and add one example or condition.
3-mark use
Explain linear polynomial in two variables, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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