MCQ Questions for Class 9 Maths Linear Equations In Two Variable Quiz 1

Which of the following equation represents a straight line which is parallel to the

$x$ -axis and at a distance

$3$ units below it?

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Any line parallel to $x$ -axis and at a distance of $3$ units below it is given by $y = 9$
0%
Any line parallel to $x$ -axis and at a distance of $3$ units below it is given by $y = -3$
0%
Any line parallel to $x$ -axis and at a distance of $3$ units below it is given by $x = -3$
0%
Any line parallel to $x$ -axis and at a distance of $3$ units below it is given by $x = 0$

Explanation

Any straight line parallel to

$x-$ axis is given by

$y=k,$ where

$k$ is the distance of the line from

$x-$ axis. Here

$k=-3,$ because it is below

$x$ axis then the equation of the line is

$y=-3$ .

State whether the given statement is true or false:

The graph of a linear equation in two variables need not be a line.

0%
True
0%
False

Explanation

Every linear equation in two variables can be written as

$y=mx+c$ .

Here, for each value of

$x$ there is a unique value of

$y$ .

Also,

$x$ &

$y$ are in direct variation.

Hence,

$\cfrac { y }{ x }$ will always remain constant.

Consequently, the graph will maintain a definite slope making it a straight line.

$\therefore$ The given statement is false.

The equation

$x = 7$ , in two variables, can be written as

0%
$1 . x + 1 . y = 7$
0%
$1. x + 0. y = 7$
0%
$0 . x + 1 . y = 7$
0%
$0 . x + 0 . y = 7$

Explanation

$x =7$ can be written as,

$1.x + 0.y =7$ as the coefficient of

$x$ is

$1$ and that of

$y$ is

$0$ .

Two points with coordinates

$(2, 3)$ and

$(2, 1)$ lie on a line. Then

$(i)$ the line is parallel to which axis?

$(ii)$ Justify your answer.

0%
$(i)$ Parallel to $x$ -axis.

$(ii)$ Since $x$ -coordinate of both the points is $2$ , both points lie on the line $y = 2$ which is parallel to $x$ -axis.
0%
$(i)$ Parallel to $y$ -axis.

$(ii)$ Since $y$ -coordinate of both the points is $2$ , both points lie on the line $y = 2$ which is parallel to $y$ -axis.
0%
$(i)$ Parallel to $y$ -axis.

$(ii)$ Since $x$ -coordinate of both the points is $2$ , both points lie on the line $x = 2$ which is parallel to $y$ -axis.
0%
$(i)$ Parallel to $x$ -axis.

$(ii)$ Since $y$ -coordinate of both the points is $2$ , both points lie on the line $x = 2$ which is parallel to $y$ -axis.

Explanation

By plotting the points on the graph, we get a line

$x=2$ which is parallel to

$y-$ axis.

Age of

$x$ exceeds the age of

$y$ by 7yrs. This statement can be expressed as the linear equation as :

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$x + y + 7 = 0$
0%
$x - y + 7 = 0$
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$x - y - 7 = 0$
0%
$x + y - 7 = 0$

Explanation

According to question,

$x-y=7$

$\Rightarrow$

$x-y-7=0$

So, option C is correct.

How many linear equations in

$x$ and

$y$ can be satisfied by

$x = 1$ and

$y = 2$ ?

0%
Only one
0%
Two
0%
Infinitely many
0%
Three

Explanation

From the graph, its clear that infinite straight lines can pass through the point (1,2).
So, infinite linear equation are possible satisfying

$x=1,y=2$

State whether the given statement is true or false:

Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

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True
0%
False

The condition that the equation

$ax + by + c = 0$ represent a linear equation in two variables is :

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$a \neq 0, b = 0$
0%
$b \neq 0, a = 0$
0%
$a = 0, b = 0$
0%
$a \neq 0, b \neq 0$

Explanation

The condition for

$ax+by+c=0$ to be a linear eqaution in two variables is

$a\neq 0\quad , b\neq 0$

The linear equation

$x = 5$ in two variables can be written as :

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$1.x + 5 = 10$
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$0.x + 1. y + ( - 5) = 0$
0%
$1.x + 0. y + ( - 5) = 0$
0%
$1.x + 1. y + ( - 5) = 0$

Explanation

$x=5$

$\Rightarrow$

$x-5=0$

$\Rightarrow$

$1.x+(-5)=0$

$\Rightarrow$

$1.x+0.y+(-5)=0$

Linear equation in one variable is :

0%
$2x = y$
0%
$y^2 = 3y + 5$
0%
$4x - y = 5$
0%
$3t + 5 = 9t- 7$

Explanation

${\textbf{Step - 1 : State the definition of linear equation with one variable}}{\text{.}}$

${\text{As per the definition , Linear equation with one variable is that equation which have,}}$

${\text{literally one variable with highest power of 1}}{\text{.}}$

${\textbf{Step - 2 : Choose the correct option using the definition}}{\text{.}}$

${\text{The first equation is 2x = y}}{\text{.Where x and y are variables}}{\text{. So there are two variable}}{\text{.}}$

$\Rightarrow {\text{This is not a linear equation in one variable}}.$

${\text{The second option is, }}{{\text{y}}^2}{\text{ = 3y + 5}}{\text{. Here there is only one variable.}}\\{\text{But the highest power is 2}}{\text{. }}$

$\Rightarrow {\text{This is not a linear equation in one variable}}.$

${\text{In third option 4x}} - {\text{y = 5}}{\text{. Here there are two variables , x and y}}{\text{.}}$

$\Rightarrow {\text{This is not a linear equation in one variable}}.$

${\text{In fourth option 3t + 5 = 9t}} - 7.{\text{ Here there is only one variable and the $\\$highest power is also 1}}{\text{. }}$

$\Rightarrow {\text{This is a linear equation in one variable}}.$

${\textbf{Thus, the linear equation with one variable is option (D) 3t + 5 = 9t}} - 7.$

Is the following equation linear in two variables?

$\displaystyle \frac{4}{x} + 3y = 14$

0%
Yes
0%
No
0%
Ambiguous
0%
Data Insufficient

Explanation

$\dfrac{4}{x} + 3y = 14$

$4 + 3xy = 14x$
The equation

$4 + 3xy = 14x$ is not of the form

$y = mx + c$ .
Hence, it is not a linear equation.
The degree of its variable is also two,
Hence the equation cannot be linear.

State true/false:

One number is 5 more than seven times the other number. It can be represented by

$x\, -\, 7y\, =\, 5$ .

0%
True
0%
False

Explanation

Let one number be

$x$ and the other number be

$y$ , then

It is given that

$x$ is

$5$ more than the seven times the other number that is

$y$ .

$x = 5+7y$

$x-7y = 5$

$4x-3=0$ is a line parallel to

0%
$y$ axis
0%
$x$ axis
0%
$y=x$
0%
$y=2x$

Explanation

Given,

$4x-3=0$

$\Rightarrow 4x=3$

$\Rightarrow x=\dfrac 34$
Since, every line of type

$x=a$ is parallel to

$y$ axis.
So, option A is correct.

Express the given information in the form of an equation in mathematical form using two variables:

The cost of two tables and five chairs is Rs. 2200.

0%
$2x\, +\, 5y\, =\, 2200$
0%
$x\, +\, 10y\, =\, 800$
0%
$10x\, -\, 5y\, =\, 1800$
0%
Insufficient data

Explanation

Let the cost of one table be

$Rs.\ x$ and that of one chair be

$Rs.\ y$ .

Hence, cost of two tables

$=Rs.\ 2x$ and cost of five chairs

$=Rs.\ 5y$

Given that, the cost of two tables and five chairs is

$Rs.\ 2200$ .

$\therefore 2x+5y=2200$

Hence, option A is correct.

Write a linear equation in two variables to represent the following statement.

The age of Jenson is less than the age of Gibin by

$6$ years

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$x + 6 = y$ , where $x =$ age of Jenson and $y =$ age of Gibin
0%
$x + 16 = y$ , where $x =$ age of Jenson and $y =$ age of Gibin
0%
$x - 6 = y$ , where $x =$ age of Jenson and $y =$ age of Gibin
0%
$x + 6 = 2y$ , where $x =$ age of Jenson and $y =$ age of Gibin

The graph of the equation

$x= b$ is also a straight line parallel to _____.

0%
$y$ -axis
0%
$x$ -axis
0%
Cannot be determined
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Not Parallel

Write the following equation as an equation in two variables:

$2x=-3$

0%
$2x + 0y + 3 = 0$
0%
$2x + 0y + 3 = 1$
0%
$2x + 2y + 3 = 0$
0%
$3x + 0y + 3 = 0$

Explanation

The given equation

$2x = -3$
It can be written as

$2.x + 0.y = -3$

$\Rightarrow 2.x + 0.y + 3 = 0$

Write a linear equation in two variables to represent each of the following statement.

5 books and 7 pens together cost Rs 79.

0%
5x + 7y = 79, where x = cost of a book and y = cost of a pen.
0%
4x + 7y = 79, where x = cost of a book and y = cost of a pen.
0%
5x + 6y = 79, where x = cost of a book and y = cost of a pen.
0%
5x - 7y = 79, where x = cost of a book and y = cost of a pen.

Explanation

The cost of 1 book

$=x$
The cost of 1 pen

$=y$
Then the linear equation is

$\Rightarrow 5x+7y=79$

Write the following equation as an equation in two variables:

$3y = 4$

0%
$0x + 3y - 4 = 0$
0%
$0x + 2y - 4 = 0$
0%
$0x + 3y - 5 = 0$
0%
$2x + 3y - 4 = 0$

Explanation

The given equation is

$3y = 4$
This can be written as

$0.x + 3.y = 4$

$\Rightarrow 0x + 3y - 4 = 0$

A straight line parallel to the

$x$ -axis has equation

0%
$x = a$
0%
$y = a$
0%
$y = x$
0%
$y = -x$

Explanation

A straight line parallel to the

$x$ axis has equation

$y=a$ .

The graph of the equation

$y = a$ is a straight line parallel to _____

0%
$x$ -axis
0%
$y$ -axis
0%
Cannot be determined
0%
Not Parallel

Write a linear equation in two variables to represent the following statement.

The cost of a pen is thrice the cost of a pencil

0%
$x = 3y,$ where $x =$ cost of a pen and $y =$ cost of a pencil.
0%
$x = 2y,$ where $x =$ cost of a pen and $y =$ cost of a pencil.
0%
$2x = 3y,$ where $x =$ cost of a pen and $y =$ cost of a pencil.
0%
$x = y$ , where $x =$ cost of a pen and $y =$ cost of a pencil.

Explanation

Let the cost of a pen be

$x$ and the cost of a pencil be

$y$
According to the statement, cost of a pen is thrice the cost of a pencil

$\Rightarrow x=3y$

$\Rightarrow x-3y=0$ which is a linear equation in two variables

Which of the following equation is not a linear equation?

0%
$2x + 3 = 7x - 2$
0%
$\displaystyle \frac{2}{3}x + 5 = 3x - 4$
0%
$\displaystyle x^2 + 3 = 5x - 3$
0%
$\displaystyle (x - 2)^2 = x^2 + 8$

Explanation

An algebraic equation is said to be linear if the variable or variables in the equation are of the first degree.

In option

$A$ , all the

$x$ terms have a degree

$1$ . So, it is a linear equation.

In option

$B$ , all the

$x$ terms have a degree

$1$ . So, it is a linear equation.

In option

$C$ ,

$x^{2}+3=5x-3, x$ is raised to the power

$2$ .
So,

$x^{2}+3=5x-3$ is not a linear equation.

In option

$D$ ,

$(x-2)^2=x^2+8$

$\Rightarrow x^2-4x+4=x^2+8$

$\Rightarrow -4x=4$
i.e, the

$x$ term has a degree

$1$ . So, it is a linear equation.

Hence, Option

$C$ is the correct option.

Write the following equations in the form ax + by + c = 0

$x - 4 = \sqrt 3 y$

0%
$x + (- \sqrt 3)y + (-4) = 0$
0%
$x + ( \sqrt 3)y + (-4) = 0$
0%
$x + (- \sqrt 3)y + (4) = 0$
0%
$2x + (- \sqrt 3)y + (-4) = 0$

Explanation

The given equation in the form

$ax + by + c = 0$

$\Rightarrow x-\sqrt{3}y-4=0$
Comparing with

$ax+by+c=0$

$\Rightarrow a=1$

$\Rightarrow b=-\sqrt{3}$

$\Rightarrow c=-4$

Any point on

$x$ axis is of the form

0%
$(x,y)$
0%
$(0,y)$
0%
$(0,0)$
0%
$(x,0)$

Explanation

$\textbf{Step 1: Writing Coordinates of given point}$

$\text{We know that any point on the x-axis}\implies y=0$

$\text{Hence, any point on the x-axis can be expressed as (x,0)}$

$\textbf{Hence, Any point on the x-axis can be expressed as of the form (x,0)}$

Write the following equation in the form of

$ax + by + c = 0$ .

$5x - 3y = 4$

0%
$5x + (-3)y + (-4) = 0$
0%
$5x + (3)y + (-4) = 0$
0%
$5x + (-3)y + (4) = 0$
0%
$4x + (-3)y + (4) = 0$

Explanation

The given equation in the form

$ax + by + c = 0$ is

$\ 5x-3y-4=0$
Comparing with

$ax+by+c=0$

$\Rightarrow a=5$

$\Rightarrow b=-3$

$\Rightarrow c=-4$

Write the following equations in the form

$ax + by + c = 0$ , where

$a= -2,b=3$ and

$c=-6$

0%
$-2x +3y -6 = 0$
0%
$x -3y + 6 = 0$
0%
$2x + 3y - 6 = 0$
0%
$2x + 3y + 6 = 0$

Explanation

The given equation in the form

$ax + by + c = 0$

$\Rightarrow -2x+3y-6=0$

$5x -3y = 5$ a linear equation in one variable?

0%
Yes
0%
No
0%
Ambiguous
0%
Data insufficient

Explanation

No, the given equation

$5x - 3y = 5$ is a linear equation in two variable having

$x$ and

$y$ as the two variables.

Write the equation

$2x = y$ in the form of

$ax + by + c = 0:$

0%
$2x + (-1)y + 0 = 0$
0%
$2x + (1)y + 0 = 0$
0%
$2x + (-1)y + 1 = 0$
0%
$x + (-1)y + 0 = 0$

Explanation

The given equation in the form

$ax + by + c = 0$ is

$2x-y+0=0$
Comparing with

$ax+by+c=0$

We have

$a=2$

$b=-1$

$c=0$

What is a linear equation in

$2$ variables?

0%
An equation containing $2$ variables raised to the power $1$
0%
An equation in which the variables are power $2$
0%
An expression containing $2$ variables
0%
None of the above

Explanation

An equation which has two variables and highest power of the variables is

$1$ is called a linear equation in 2 variables.

i.e An equation containing 2 variables raised to the power is a linear equation in 2 variables.

Hence, option A is correct.

CBSE Questions for Class 9 Maths Linear Equations In Two Variable Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Linear Equations In Two Variable Quiz 1 - MCQExams.com

0:0:1

Practice Class 9 Maths Quiz Questions and Answers

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