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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-03-GRA-01
Graphical Solution — Assignment
Chapter: Pair of Linear Equations
Topic: Graphical Solution
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Two lines intersecting at one point give:
  • A.no solution
  • B.a unique solution
  • C.infinitely many
  • D.none
2.
Parallel lines give:
  • A.unique
  • B.no solution
  • C.infinitely many
  • D.two
3.
Coincident lines give:
  • A.unique
  • B.no solution
  • C.infinitely many
  • D.two
4.
Condition for a unique solution:
  • A.$\tfrac{a_1}{a_2}\ne\tfrac{b_1}{b_2}$
  • B.$\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}$
  • C.$\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}=\tfrac{c_1}{c_2}$
  • D.none
5.
Condition for infinitely many solutions:
  • A.$\tfrac{a_1}{a_2}\ne\tfrac{b_1}{b_2}$
  • B.$\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}=\tfrac{c_1}{c_2}$
  • C.$\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}\ne\tfrac{c_1}{c_2}$
  • D.always
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
State the ratio condition for no solution.
7.
Do $x+y=2$ and $x+y=5$ have a solution?
8.
How many solutions do $x+y=4$ and $2x+2y=8$ have?
9.
Is $(1,1)$ a solution of $x+y=2$?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State the nature of solutions of $x-y=1$ and $2x-2y=2$.
11.
Determine the nature of solutions of $2x+3y=7$ and $4x+6y=12$.
12.
State the nature of solutions of $x+2y=4$ and $3x+6y=12$.
13.
Solve graphically $x+y=5$ and $x-y=1$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve graphically $x+y=7$ and $3x-y=1$, and find the point of intersection.
15.
For what value of $k$ do $kx+3y=k-3$ and $12x+ky=k$ have no solution?

Answer Key

Section A — Multiple Choice Questions
  1. (B) a unique solution
  2. (B) no solution
  3. (C) infinitely many
  4. (A) $\tfrac{a_1}{a_2}\ne\tfrac{b_1}{b_2}$
  5. (B) $\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}=\tfrac{c_1}{c_2}$
Section B — Short Answer (2 marks)
  1. $\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}\ne\tfrac{c_1}{c_2}$.
  2. No (parallel lines).
  3. Infinitely many.
  4. Yes.
Section C — Short Answer (3 marks)
  1. Coincident — infinitely many solutions.
  2. No solution (parallel).
  3. Infinitely many.
  4. $(3,2)$.
Section D — Long Answer (5 marks)
  1. $(2,5)$.
  2. $k=-6$.
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