1. Find the x-intercept of 5x − 2y = 10.
- A2
- B−5
- C10
- D5
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Answer: A) 2
Set y = 0: 5x = 10 → x = 2.
Class 9 Linear Equations in Two Variables — practice questions with answers
Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. At what point does the graph of 2x + 3y = 6 cut the x-axis?
- A(3, 0)
- B(0, 2)
- C(2, 0)
- D(0, 3)
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Answer: A) (3, 0)
It cuts the x-axis where y = 0: 2x = 6 → x = 3, giving (3, 0).
3. A line passes through the points (0, 4) and (4, 0). Which equation represents it?
- Ax + y = 4
- Bx − y = 4
- Cx + y = 0
- Dx + 4y = 4
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Answer: A) x + y = 4
Test x + y = 4: (0,4) → 0+4=4 ✓ and (4,0) → 4+0=4 ✓. Both points satisfy it.
4. For 3x − 4y = 15, express x in terms of y.
- Ax = 15 + 4y
- Bx = (15 − 4y)/3
- Cx = (4y − 15)/3
- Dx = (15 + 4y)/3
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Answer: D) x = (15 + 4y)/3
−4y moves across as +4y: 3x = 15 + 4y, then divide everything by 3 → x = (15 + 4y)/3. Check with y = 0: x = 5, and 3(5) − 0 = 15 ✓.
5. A shopkeeper sells x kg of rice and y kg of wheat, 40 kg in all, so x + y = 40. Where does the graph of this equation meet the y-axis, and what does that point mean?
- A(40, 0) — he sold no rice and 40 kg of wheat
- B(0, 40) — he sold 40 kg of rice and no wheat
- C(20, 20) — he sold equal amounts of each
- D(0, 40) — he sold no rice and 40 kg of wheat
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Answer: D) (0, 40) — he sold no rice and 40 kg of wheat
The graph meets the y-axis where x = 0, so 0 + y = 40 gives the point (0, 40). Since x stands for the rice, x = 0 means no rice was sold and the whole 40 kg was wheat.
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