Vidaara.orgClass 10 · Mathematics
CodeVID-M10-03-CT
Pair of Linear Equations in Two Variables — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
In substitution we express:
- A.both as constants
- B.one variable in terms of the other
- C.the sum
- D.nothing
3.
The sum of two numbers is $30$, difference $6$. The numbers are:
- A.$20,10$
- B.$18,12$
- C.$15,15$
- D.$24,6$
4.
Parallel lines give:
- A.unique
- B.no solution
- C.infinitely many
- D.two
5.
The three methods include substitution, elimination and:
- A.graphing
- B.cross-multiplication
- C.trial
- D.division
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
State the ratio condition for no solution.
7.
Solve $x+y=6,\ x-y=2$.
8.
The sum of two numbers is $25$ and difference $7$. Find them.
9.
Do $x+y=2$ and $x+y=5$ have a solution?
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.
Solve by substitution: $2x+3y=12,\ x-y=1$.
12.
The larger of two numbers exceeds the smaller by $8$ and their sum is $50$. Find them.
13.
Determine the nature of solutions of $2x+3y=7$ and $4x+6y=12$.
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.
Solve $2x+3y=11$ and $2x-4y=-24$; then find $m$ if $y=mx+3$.
Answer Key
Section A — Multiple Choice Questions
- (B) a unique solution
- (B) one variable in terms of the other
- (B) $18,12$
- (B) no solution
- (B) cross-multiplication
Section B — Short Answer (2 marks)
- $\tfrac{a_1}{a_2}=\tfrac{b_1}{b_2}\ne\tfrac{c_1}{c_2}$.
- $x=4,\ y=2$.
- $16$ and $9$.
- No (parallel lines).
Section C — Short Answer (3 marks)
- Coincident — infinitely many solutions.
- $x=3,\ y=2$.
- $29$ and $21$.
- No solution (parallel).
Section D — Long Answer (5 marks)
- $(2,5)$.
- $x=-2,\ y=5,\ m=-1$.
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