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9th CBSE Mathematics Unit 4 Linear Equations in Two Variables Important Question Paper

Published on: 30/07/2019

Linear Equations in Two Variables

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Std: 9th Standard CBSE - Mathematics

chapter: - Model Question paper

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Questions:

Generic 3

2 x 3 = 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:
x=3y

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

Write six solutions for the equation 2x+y=7

Find four different solutions of the equation x + 2y = 6

Find three different solutions for the equation 6x-8y+32=0

Write the following as an equation in two variables:
2x=3

Write the following as an equation in two variables:
x=-5

Generic 4

2 x 4 = 8

In an election, a good candidate may lose because 40% of voters do not cast their votes due to various reasons. Form an equation and draw the graph with data. Form the graph, Find:
(i) the total number of voters, if 300 voters cast their votes
(ii) the number of votes cast, if the total number of voters are 1000.
(iii) What is its value.

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

10 x 1 = 10

10.

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

11.

The opposite angles of a parallelogram are equal.Write a linear equation in two variables to represent the statement

(a)

x+y=0

(b)

x=y

(c)

x=2y

(d)

x+y+1=0

12.

The salary of Dr.Harikisham is thrice the salary of Manish Goyal.Write a linear equation in two variables to represent the statement.

(a)

x=3

(b)

x+3y=0

(c)

x=3y+3

(d)

x=y+3

13.

Cost of book (x) exceeds twice the cost of pen (y) by Rs,10.This statement can be expressed as linear equation:

(a)

x-2y-10=0

(b)

2x-y-10=0

(c)

2x+y-10=0

(d)

x-2y+10=0

14.

The equation in 3x+4y=12 has

(a)

a unique solution

(b)

no solution

(c)

two solution

(d)

infinitely may solution

15.

Write a, b, c for the equation 2y-x=7

(a)

-1,2,-7

(b)

1,2,7

(c)

-1,-2,-7

(d)

-1,-2,7

16.

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

(a)

1,1,0

(b)

1,-1,0

(c)

-1,1,0

(d)

1,-1,1

17.

Write a, b, c for the equation 2x=5

(a)

2, 0, -5

(b)

0,2,-5

(c)

0,0,-5

(d)

2,0,5

18.

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

(a)

no solution

(b)

infinitely many solutions

(c)

only one solution

(d)

only two solution

19.

\(\sqrt{2}y+ \sqrt{3}=0\) is

(a)

a linear equation in one variable

(b)

not a linear equation in one variable

(c)

a linear equation in two variables

(d)

none of these

1 Marks

5 x 1 = 5

20.

If \(\sqrt { 3 } x=\sqrt { 2 } x+1\) , then x is equal to _____

21.

Find the point where equation 3x+2y=12 intersects y-axis

22.

If the linear equation has solutions (-5,0),(0,0),(5,-5) then the equation is ______

23.

Is x=4, y=0, the solution of y-4=0?

24.

Is ox+oy+c=0, a linear equation?

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Answers Key:

Generic 3

2 x 3 = 6

x=3y
x-3y+0=0
Comparing with ax+by+c=0, we get
a=1, b=-3, c=0.

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

Generic 2

5 x 2 = 10

(0,7), (1,5), (2,3), (3,1), (4, -1), (5,-3)

By inspection, x = 2, y = 2 is a solution because for x = 2, y = 2
x + 2y = 2 + 4 = 6
Now, let us choose x = 0. With this value of x, the given equation reduces to 2y = 6 which has the unique solution y = 3. So x = 0, y = 3 is also a solution of x + 2y = 6. Similarly, taking y = 0, the given equation reduces to x = 6. So, x = 6, y = 0 is a solution of x + 2y = 6 as well. Finally, let us take y = 1. The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Therefore, (4, 1) is also a solution of the given equation. So four of the infinitely many solutions of the given equation are:
(2, 2), (0, 3), (6, 0) and (4, 1).

(0,3), (4,6), (-4,0)

2x+0y-3=0

1x+0y+5=0

Generic 4

2 x 4 = 8

Since total number of voters who do not cast therir cotes=40%
Hence total number of voters who cast their votes =60%
Let the total numbers of voters are x and number of voters who cast their votes is y.
Then according to the question
y=60% of \(x=\frac{60}{100}x\)
Now, when c=100, then
y=60
when x=200, then y=120
when c=300, then y=180

x	100	200	300
y	60	120	180

By plotting the points (100,60), (200,120) (300,180) on the graph and by joining them, we get the graph of equation (1) as shown in fig. From the graph, we see that
(i) If 300 voters cast their votes, then total number of votes=500

(ii) If the total number of voters are 1000, then number of votes cast=600.
(iii) Everyone should cast his vote to elect an honest candidate.

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.

Multiple Choice Question

10 x 1 = 10

10.

(a)
x=y-1

11.

(b)
x=y

12.

(a)
x=3

13.

x=2y+10 ⇒ x-2y-10=0

14.

(d)
infinitely may solution

15.

-x+2y-7=0

16.

x+y+0=0

17.

2x+0y-5=0

18.

19.

(a)
a linear equation in one variable

1 Marks

5 x 1 = 5

20.

()
Given, \(\sqrt { 3 } x=\sqrt { 2 } x+1\)
\(\therefore \ x(\sqrt { 3 } -\sqrt { 2 } )=1\)
\(\therefore \ x=\frac { 1 }{ \sqrt { 3 } -\sqrt { 2 } } \).

21.