1. The graph of a linear equation in two variables is always a:
- AStraight line
- BParabola
- CCircle
- DCurve
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Answer: A) Straight line
Any equation of the form ax + by + c = 0 (a, b not both zero) plots as a straight line.
Class 10 Graphical Method — 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. The lines x = 5 and y = 2 are graphed. At what point do they intersect?
- A(5, 2)
- B(2, 5)
- C(5, 0)
- D(0, 2)
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Answer: A) (5, 2)
x = 5 and y = 2 hold simultaneously only at the point (5, 2).
3. The graph below shows two lines that never meet. The number of solutions of this pair is:
- A1
- B2
- C-1
- D0
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Answer: D) 0
Parallel lines drawn on the same axes never intersect, so there is no common point: 0 solutions.
4. The lines 2x + y = 6 and x = 1 are drawn. They enclose, with the x-axis, a region.
First find where 2x + y = 6 meets x = 1: what is the y-value there?
First find where 2x + y = 6 meets x = 1: what is the y-value there?
- A8
- B4
- C5
- D3
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Answer: B) 4
At x = 1: 2(1) + y = 6, so y = 4. The lines meet at (1, 4).
5. Three lines are graphed: x + y = 6, x - y = 2, and y = 1.
The first two meet at (4, 2). Do all three lines pass through that single point (4, 2)?
The first two meet at (4, 2). Do all three lines pass through that single point (4, 2)?
- ANo, because y = 1 does not pass through (4, 2)
- BYes, all three meet at (4, 2)
- CYes, because they are all straight lines
- DNo, because the lines are parallel
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Answer: A) No, because y = 1 does not pass through (4, 2)
The first two meet at (4, 2). But y = 1 requires y = 1, while the point has y = 2, so y = 1 does not pass through (4, 2). The three lines are not concurrent.
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