Q1.Graphical MeaningEasy · 1m
What does it mean geometrically when a pair of linear equations has infinitely many solutions?
Answer: The two lines coincide — they are exactly the same line.
Class 10 · Maths · Important Questions
Pair of Linear Equations in Two Variables — Important Questions
Q2.ConsistencyMedium · 2m
For what condition does a pair of linear equations have a unique solution?
Answer: When a₁/a₂ ≠ b₁/b₂ — the lines intersect at exactly one point.
Q3.No SolutionMedium · 2m
Show that the pair 2x + 3y = 5 and 4x + 6y = 15 has no solution.
Answer: a₁/a₂ = 2/4 = 1/2, b₁/b₂ = 3/6 = 1/2 but c₁/c₂ = 5/15 = 1/3. Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel and there is no solution.
Q4.SubstitutionMedium · 3m
Solve x + y = 10 and x − y = 4 by elimination.
Answer: Adding: 2x = 14 ⇒ x = 7; then y = 3. Solution (7, 3).
Q5.Word ProblemHard · 3m
The sum of two numbers is 20 and their difference is 6. Form the equations and find the numbers.
Answer: x + y = 20 and x − y = 6 ⇒ adding gives 2x = 26, x = 13 and y = 7.
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