Linear Equations in Two Variables — Previous Year Questions (Class 9 Mathematics)
Linear equations in two variables describe straight-line relationships. Learn to solve systems algebraically and graphically, and apply them to real-world
TL;DR: Linear equations in two variables describe straight-line relationships. Learn to solve systems algebraically and graphically, and apply them to real-w…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Linear equations in two variables describe straight-line relationships. Learn to solve systems algebraically and graphically, and apply them to real-world
Linear Equations in Two Variables — Previous Year Questions with Solutions
Q (2023, 2 marks): Solve the system: 2x + y = 7 and x - y = 2 using substitution method.
Answer: From equation 2: x = y + 2
Substitute in equation 1:
2(y + 2) + y = 7
2y + 4 + y = 7
3y = 3
y = 1
x = 1 + 2 = 3
Solution: x = 3, y = 1
Q (2022, 3 marks): Solve using elimination method: 3x + 2y = 11 and 5x - 4y = 1
Answer: Multiply first equation by 2: 6x + 4y = 22
Add to second equation: 5x - 4y = 1
11x = 23
x = 23/11
Substitute back: 3(23/11) + 2y = 11
69/11 + 2y = 11
2y = 121/11 - 69/11 = 52/11
y = 26/11
Solution: x = 23/11, y = 26/11
Q (2023, 3 marks): A father is 40 years old and his son is 10 years old. After how many years will the father's age be three times the son's age?
Answer: Let the number of years be x
Father's age after x years: 40 + x
Son's age after x years: 10 + x
According to condition: 40 + x = 3(10 + x)
40 + x = 30 + 3x
10 = 2x
x = 5
After 5 years, father will be 45 and son will be 15.
Verification: 45 = 3 × 15 ✓
Q (2021, 2 marks): For what value of k does the system 2x + 3y = 5 and 4x + 6y = k have infinitely many solutions?
Answer: For infinitely many solutions, the equations must be proportional.
Second equation should be 2 times the first:
4x + 6y = 2(2x + 3y) = 2(5) = 10
Therefore, k = 10
Q (2022, 3 marks): The perimeter of a rectangle is 56 cm. If its length is 4 cm more than its width, find the dimensions.
Answer: Let width = x, length = x + 4
Perimeter = 2(length + width) = 56
2(x + 4 + x) = 56
2(2x + 4) = 56
4x + 8 = 56
4x = 48
x = 12
Width = 12 cm, Length = 16 cm
Verification: 2(16 + 12) = 2(28) = 56 ✓
Q (2023, 5 marks): Solve graphically: x + y = 4 and 2x - y = 5. Also verify your solution algebraically.
Answer: From x + y = 4: y = 4 - x
Points: (0, 4), (4, 0), (1, 3), (2, 2)
From 2x - y = 5: y = 2x - 5
Points: (0, -5), (5, 5), (3, 1), (4, 3)
Graphically, lines intersect at (3, 1)
Algebraic verification:
From equation 1: y = 4 - x
Substitute in equation 2: 2x - (4 - x) = 5
2x - 4 + x = 5
3x = 9
x = 3, y = 1
Solution: x = 3, y = 1
Frequently Asked Questions
What does it mean when a system has no solution?
When lines are parallel, they never intersect, so there is no solution. Algebraically, this happens when the equations give a contradiction (e.g., 0 = 5).
How many solutions can a system of two linear equations have?
Three possibilities: (1) Unique solution (lines intersect at one point), (2) No solution (parallel lines), (3) Infinitely many solutions (identical lines).
More Class 9 Mathematics PYQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →