1. Solve: x + y = 10 and x − y = 4.
- Ax=7, y=3
- Bx=6, y=4
- Cx=5, y=5
- Dx=8, y=2
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Answer: A) x=7, y=3
Add: 2x = 14 → x = 7. Then y = 10 − 7 = 3.
Class 10 Pair of Linear Equations in Two Variables — practice questions with answers
Algebra — Systems of Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Solve: 5x − 3y = 1 and 2x + 3y = 13.
- Ax=2, y=3
- Bx=3, y=2
- Cx=1, y=4
- Dx=4, y=1
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Answer: A) x=2, y=3
Add the equations to eliminate y: 7x = 14 → x = 2. Then 2(2) + 3y = 13 → 3y = 9 → y = 3.
3. A pair of linear equations which is consistent and has infinitely many solutions is also called a:
- ADependent pair
- BIndependent pair
- CInconsistent pair
- DParallel pair
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Answer: A) Dependent pair
A consistent system with infinitely many solutions (coincident lines) is called a dependent pair of equations.
4. The two lines drawn for a pair of equations are found to have the SAME slope but DIFFERENT y-intercepts. The pair is:
- AConsistent with a unique solution
- BConsistent with infinitely many solutions
- CInconsistent, with no solution
- DConsistent with exactly two solutions
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Answer: C) Inconsistent, with no solution
Equal slopes make the lines parallel; different y-intercepts keep them apart, so they never meet and there is no common point — the pair is inconsistent. Equal slopes AND the same intercept would give one line (infinitely many solutions), and two straight lines can never cross at exactly two points.
5. Nisha's marks in Mathematics and Science add up to 90. If she had scored 5 marks more in Mathematics and 5 marks fewer in Science, her Mathematics marks would have been twice her Science marks. How many marks did she score in Science?
- A35
- B55
- C45
- D30
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Answer: A) 35
Let Mathematics = m and Science = s. Then m + s = 90 and m + 5 = 2(s − 5) → m = 2s − 15. Substituting: 2s − 15 + s = 90 → 3s = 105 → s = 35 and m = 55. Check: 55 + 35 = 90 ✓ and 60 = 2 × 30 ✓. Answering 55 gives the Mathematics marks, and 45 assumes the two subjects were equal, which ignores the second condition entirely.
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