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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-04-CT
Linear Equations in Two Variables — Full Chapter Test
Chapter: Linear Equations in Two Variables
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
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.
A linear equation in two variables is:
  • A.$ax+by+c=0$
  • B.$ax^2+bx+c=0$
  • C.$ax+b=0$
  • D.$\tfrac1x+y=0$
2.
The graph of a linear equation in two variables is a:
  • A.curve
  • B.straight line
  • C.circle
  • D.point
3.
Word problems are modelled by:
  • A.inequalities
  • B.linear equations
  • C.graphs
  • D.ratios
4.
The degree of such an equation is:
  • A.$0$
  • B.$1$
  • C.$2$
  • D.$3$
5.
The graph of $x=3$ is parallel to the:
  • A.x-axis
  • B.y-axis
  • C.line $y=x$
  • D.origin
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Is $(1,1)$ a solution of $x+y=2$?
7.
What is the graph of $x+y=4$?
8.
Write the cost of $x$ pens at $\textsf{Rs }5$ each.
9.
Write $2x=5$ in the form $ax+by+c=0$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find two solutions of $x+y=7$.
11.
Give two points to draw the line $x+y=5$.
12.
The cost of $2$ kg apples and $1$ kg grapes is $\textsf{Rs }160$. Write the equation.
13.
Express $3x+4y=12$ with $y$ in terms of $x$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find four solutions of $2x+y=7$.
15.
Draw the graph of $2x+y=6$ using its intercepts.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $ax+by+c=0$
  2. (B) straight line
  3. (B) linear equations
  4. (B) $1$
  5. (B) y-axis
Section B — Short Answer (2 marks)
  1. Yes.
  2. A straight line.
  3. $5x$.
  4. $2x+0y-5=0$.
Section C — Short Answer (3 marks)
  1. e.g. $(0,7)$ and $(3,4)$.
  2. $(0,5)$ and $(5,0)$.
  3. $2a+g=160$.
  4. $y=\tfrac{12-3x}{4}$.
Section D — Long Answer (5 marks)
  1. $(0,7),(1,5),(2,3),(3,1)$.
  2. A straight line through $(3,0)$ and $(0,6)$.
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