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Linear Equations In Two Variables - Important Questions Model Question Paper 1 In 9th Maths

Published on: 30/07/2018

Based on the chapter Linear Equations in Two Variables, some of the important questions are prepared in this question paper.

Download CBSE Class 9th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 9th Standard CBSE Mathematics

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Std: 9th Standard CBSE - Mathematics

chapter: - Model Question paper

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Questions:

Generic 3

5 x 3 = 15

A rectangle field has to be cut out and its boundary marked with fencing with a given wire of length 100m.
(a)Represent the above situation using a linear equation
(b)Also plot its graph

Consider the point A(-2, 3)
(I) How many lines can be drawn passing through A?
(ii) Give equation of any two lines passing through A.
(iii) Without actually drawing the graph, find a point, other than A, on each of these two lines.

From the choices given below, choose the equation whose graphs are given in Fig.(1) and Fig.(2)
For Fig.1 For Fig.2
(i)y=x (i)y=x+2
(ii)x+y=0 (ii)y=x-2
(iii)y=2x (iii)y=-x+2
(iv)x+3y=7x (iv)x+2y=6

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
5=2x

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
\(x-{y\over 5}-10=0\)

Generic 2

5 x 2 = 10

Give the geometrical representation of the equation 3x + 15 = 0 as an equation:
(i) in one variable
(ii) in two variables.

The parking charges of a car on New Delhi Railway Station for first two hours is Rs.50 and Rs.10 for subsequent hours.Write down an equation and draw the graph of this data. Read the charges from the graph:
(i) for one hour
(ii) for three hours
(iii) for six hours.

Write the following equations in the form ax+by+c=0 and indicate the values of a, b and c
\(x-4=\sqrt{3}y\)

Write the following as an equation in two variables:
5y=2

10.

Write the following as an equation in two variables:
y=2

Generic 4

5 x 4 = 20

11.

Solve for x:
\(3x-12+{3\over7}x=2(x-1)\)
What type of graph is it in two dimensions?

12.

Rohit is driving his car at a uniform speed of 80 km per hour. Draw time-distance graph taking time along x-axis and distance along y-axis.

13.

Draw the graph of the equations x = 3 and 4x = 3y in the same graph.Find the area of the triangle formed by these two lines and the x-axis

14.

Find the coordinates of the points where the line representing the equation \({x\over4}=1-{y\over 6}\)cuts the x-axis and the y-axis

15.

Express x=3y in the form ax+by+c=0 and indicate the values of a, b and c.Write two solutions of the equation.

Multiple Choice Question

5 x 1 = 5

16.

The numerator of a fraction is 1 less than the denominator.Write a linear equation in two variables to represent the statement.

(a)

x=y-1

(b)

x+y=0

(c)

x=y

(d)

x+y+1=0

17.

The sum of the ages of Apala and Meenu is 48.Write a linear equation in two variables to represent the statement.

(a)

x+y=48

(b)

x-y-10=0

(c)

2x+y=48

(d)

x+2y=48

18.

The equation 2x=3 in two variables is of the form:

(a)

2.x+3.y=0

(b)

2.x+0.y=3

(c)

\({2\over3}.x+0.y=3\)

(d)

1.x+\(2\over3\).y=1

19.

Write a, b, c for the equation 3y+4=0

(a)

0,3,4

(b)

3,0,4

(c)

4,0,3

(d)

4,3,0

20.

The equation \(x+\sqrt{2}=0\) has

(a)

no solution

(b)

infinitely many solutions

(c)

only one solution

(d)

only two solution

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Answers Key:

Generic 3

5 x 3 = 15

(a)x+y=50

(i)Infinitely many
(ii)x+y1=0, -x+y=5
(iii)(0,-1), (0, 5)

For Fig. (1). The correct equation is
(ii) x + y = 0 as (-1, 1), (0, 0) and (1, -1) satisfy the equation x + y = O.
For Fig. (2). The correct equation is
(iii) y = - x + 2 as (-1, 3), (0, 2) and (2, 0) satisfy the equation y = - x + 2.

⇒ -2x+5=0
⇒ -2x+0.y+5=0
Comparing with ax+by+c=0, we get
a=-2, b=0, c=5

\(x-{y\over 5}-10=0\)
Comparing with ax+by+c=0, we get
a=1, b=\(-{1\over 5 }\), c=-10

Generic 2

5 x 2 = 10

3x+15=0
\(\Rightarrow\) x=-5

(ii) Equation in one variable (Number line) : A point P at a distance of 5 units to left of 0 on the number
line.
(iii) In two variables (Cartesian plane) : A line AB parallel to y-axis at a distance of 5 units to the left of
y-axis.

y = SO+ lO(x - 2), where x > 2
⇒ y = 30 + lOx, where x > 2
(i) Rs.50 (ii) Rs.60, (iii) Rs.90

\(x-4=\sqrt{3}y\)=0; a=2, b=\(-\sqrt{3}\), c=-4

0x+5y-2=0

10.

0x+1y-2=0

Generic 4

5 x 4 = 20

11.

\(3x-12+{3\over7}x=2(x-1)\)
\(\Rightarrow\ \ {24\over7}x-12=2x-2\)
\(\Rightarrow\ \ \ {24\over 7}x-2x=12-2\)
\(\Rightarrow\ \ \ {10x\over 7}=10\)
\(x=7\)
The graph of this equation is a line parallel to y-axis at a distance of 7 units to the right of origin O.

12.

Let us represent time (in hour) by x and distance (in km) by y. Then, we have y =80x.
Table of solution

x	1	2	3	4
y	80	160	240	320

We plot the points (1, 80), (2, 160), (3, 240) and (4, 320) on a graph paper and join these points by a ruler to get the line which is the graph of the equation y = 80x.

13.

x = 3 represents a line parallel to y-axis at a distance of 3 units to the right of the origin.
4x= 3y
\(\Rightarrow\ \ \ y={4x\over 3}\)
Table of solution

x	0	3
y	0	4

We plot the points (0,0) and (3, 4) on a graph paper and join the same by a ruler to get the line which is the graph of the equation 4x = 3y.

Area of the triangle GAB formed by the given two lines and the x-axis \(={3\times 4\over2}=6\) square units

14.

\({x\over4}=1-{y\over6} \)
For intersection with the x-axis, put y=0
\(\therefore {x\over4}=1\ \Rightarrow\ x=4\)
Hence the point of intersection with the x-axis is (4,0)
For intersection with the y-axis, put x=0
\(\therefore1-{y\over 6}=0\Rightarrow{y\over 6}=1\Rightarrow y=6\)
Hence the point of intersection with the y-axis is (0, 6)

15.

x=3y
x-3y=0
(1)x+(-3)y+(0)=0
Comparing with ax+by+c=0, we get
a=1
b=-3
c=0
Now x=3y
\(\Rightarrow\ \ \ y={x\over 3}\)
Put x=0, then \(y={0\over3}=0\)
Put x=3, then \(y={3\over 3}=1\)
Hence, (0, 0) and (3, 1) are the two solutions of the equation x=3y.