Linear Equations in Two Variables – MCQs (PYQs Level)
By Home Academy | NDA, NTSE & Other Competitive Exams Practice Set
👉 Concept Reminder:
A linear equation in two variables is of the form ax + by + c = 0, where a, b, c are real numbers and a, b ≠ 0 (at least one must be non-zero).
MCQ Practice Set
1. (NDA Level)
If 2x + 3y = 12 and x = 3, then the value of y is:
A) 1
B) 2
C) 3
D) 4
Answer: ✅ B) 2
(2×3 + 3y = 12 → 6 + 3y = 12 → 3y = 6 → y = 2)
2. (NTSE Level)
Which of the following represents a linear equation in two variables?
A) x² + y = 5
B) xy + 3 = 0
C) 4x – 7y = 9
D) y² = x + 1
Answer: ✅ C) 4x – 7y = 9
3. (NDA PYQ Type)
The pair of equations 3x + 2y = 5 and 6x + 4y = 10 has:
A) No solution
B) Unique solution
C) Infinitely many solutions
D) Exactly two solutions
Answer: ✅ C) Infinitely many solutions
(Second equation is double of first → Same line)
4. (NTSE Type)
The graph of a linear equation in two variables is always:
A) Circle
B) Parabola
C) Straight line
D) Hyperbola
Answer: ✅ C) Straight line
5. (NDA Previous Year Pattern)
If the point (2, –1) satisfies the equation ax + by = 5 and a = 2, then the value of b is:
A) –1
B) 1
C) –2
D) 2
Answer: ✅ A) –1
(2×2 + b×(–1) = 5 → 4 – b = 5 → b = –1)
6. (NTSE PYQ Type)
For what value of k will the equation 2x + ky = 8 represent a line parallel to 4x + 6y = 10?
A) 3
B) 2
C) 6
D) 12
Answer: ✅ A) 3
(Parallel lines → a₁/a₂ = b₁/b₂ → 2/4 = k/6 → 1/2 = k/6 → k = 3)
7. (NDA Level)
If x = 2 is a solution of the equation 5x + 3y = 19, find y.
A) 2
B) 3
C) 4
D) 5
Answer: ✅ B) 3
(5×2 + 3y = 19 → 10 + 3y = 19 → 3y = 9 → y = 3)
8. (NTSE Type)
The system of equations
2x + 3y = 7
4x + 6y = 15
has:
A) Unique solution
B) Infinitely many solutions
C) No solution
D) Exactly two solutions
Answer: ✅ C) No solution
(2x + 3y = 7
Multiply by 2 → 4x + 6y = 14 ≠ 15 → Parallel lines)
9. (NDA Pattern)
The intercepts of the line 2x + y = 4 on x-axis and y-axis are:
A) (2,0) and (0,4)
B) (4,0) and (0,2)
C) (0,2) and (4,0)
D) (1,0) and (0,4)
Answer: ✅ A) (2,0) and (0,4)
(If y = 0 → x = 2; If x = 0 → y = 4)
10. (NTSE PYQ Type)
If two linear equations have different slopes, then they:
A) Are parallel
B) Coincide
C) Intersect at one point
D) Have no solution
Answer: ✅ C) Intersect at one point
📌 Important Exam Points (NDA / NTSE / SSC)
✔ Condition for Unique Solution → a₁/a₂ ≠ b₁/b₂
✔ Condition for Infinite Solutions → a₁/a₂ = b₁/b₂ = c₁/c₂
✔ Condition for No Solution → a₁/a₂ = b₁/b₂ ≠ c₁/c₂
✔ Graph of linear equation → Straight Line
✔ Degree of linear equation → 1
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