Pair of linear equations in two variables
A pair of linear equations in two variables is two first-degree equations written together, such as ax + by + c = 0 and px + qy + r = 0, with the same two unknowns.
Practice This ConceptMain explanation
Teacher explanation
This chapter studies two equations together because many real problems need two conditions to be satisfied at the same time. The solution is the ordered pair of values of x and y that makes both equations true. In exams, students must learn to identify the type of pair and choose a suitable method quickly.
Example
For example, 2x + y = 7 and x - y = 1 form a pair of linear equations in two variables. Their common solution is the pair that satisfies both equations.
Simple analogy
Think of the two equations as two rules and the solution as the one pair that obeys both rules together.
Common confusion
Many students treat the two equations separately and write two different answers. That is wrong because the correct answer must satisfy both equations together.
Exam tip
Always write both equations clearly first, then decide whether graphing, substitution, or elimination will be fastest for the given question.
Study the pair of linear equations in two variables diagram carefully
Use the labelled diagram to keep pair of linear equations in two variables clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of pair of linear equations in two variables in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on pair of linear equations in two variables.
Revision cue
Revise pair of linear equations in two variables through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of pair of linear equations in two variables in one clean line.
2-mark use
Define pair of linear equations in two variables and add one example or condition.
3-mark use
Explain pair of linear equations 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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