MCQ Questions for Class 9 Maths Linear Equations In Two Variable Quiz 3

Graph of linear equation

$4x = 5$ in a plane is:

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Parallel to $x -axis$
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Parallel to $y- axis$
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Lies along $x - axis$
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Passes through origin

Explanation

Given equation is

$4x=5$

$\Rightarrow$

$x=\dfrac{5}{4}$

Also, we know that line

$x=k$ is always parallel to

$y$ -axis.

$\therefore x=\dfrac{5}{4}$ is parallel to

$y$ -axis.

A bag with total

$10$ balls contains

$x$ blue and

$y$ red balls. If the number of blue balls is four times the number of red, then write the two equations.

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$x+y=10, x=4y$
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$x-y=10, x=4y$
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$xy=10, x+4y=0$
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None of these

Explanation

Since total number of balls is

$10$ and only blue

$(x)$ and red balls

$(y)$ are there in the bag.

$\Rightarrow x+y=10$

and number of blue balls is four time the number of red balls so,

$x = 4y$

Hence option

$A$ is correct choice

Which of the following is not a linear equation in two variables?

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$x=3y-1$
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$y=2x+3$
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$x^2 - 5 =0$
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$x-y =0$

Explanation

Linear equations in two variables means the overall degree of the equation should be $1$ .

But in $(x^2-5=0)$ there is only one degree variable $x$ . Also the degree of equation is $2$ .

Draw the graphs of linear equations

$y = x$ and

$y =- x$ on the same cartesian plane. What do you observe?

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Graph of each equation is a line passing through $(1, 1)$ .
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Graph of each equation is a line passing through $(0, 1)$ .
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Graph of each equation is a line passing through $(0, 0)$ .
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Graph of each equation is a line passing through $(1, 0)$ .

Draw the graph for the linear equation

$3y+5=0$ and select the correct option:

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The line is parallel to the $x$ -axis and passes through $\left (0, -\dfrac{5}{3}\right)$
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The line is parallel to the $y$ -axis and passes through $\left (0, -\dfrac53\right)$
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The line is parallel to the $x$ -axis and passes through $\left (0, \dfrac53\right)$
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The line is parallel to the $y$ -axis and passes through $\left (0, \dfrac53\right)$

State true/false:

Two years hence, father's age will be twice the son's age then, it can be represented by

$x\, -\, 2y\, =\, 2$ .

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True
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False

Explanation

Let the father's present age be

$x$ and son's present age be

$y$
Then, after

$2$ years father's age

$= x + 2$
and Son's age

$= y + 2$

ATQ

$(x + 2) = 2(y+2)$

$\Rightarrow x + 2 = 2y + 4$

$\Rightarrow x - 2y = 4 -2$

$\Rightarrow x - 2y = 2$

Hence,

$True$

The graph of

$x =8$ represents:

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line parallel to $y$ -axis and at a distance of $8$ units.
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line parallel to $x$ -axis and at a distance of $8$ units.
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line parallel to $y$ -axis and at a distance of $0$ units.
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None of these

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

In a one-day International cricket match between India and Sri Lanka, the two teams together scored 679 runs.

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$x + y = 679,$ where $x =$ runs scored by india and $y =$ runs scored by sri lanka
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$x - y = 679,$ where $x =$ runs scored by india and $y =$ runs scored by sri lanka
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$2x + y = 679,$ where $x =$ runs scored by india and $y =$ runs scored by sri lanka
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$x + 2y = 679,$ where $x =$ runs scored by india and $y =$ runs scored by sri lanka

Explanation

Let runs scored by India

$=x$
Runs scored by Sri lanka

$=y$

given

$x+y = 679$

Then the linear equation representing the given statement

$\Rightarrow x+y=679$

Say true or false:

The following equation is an example of a linear equation in two variables:

$\displaystyle \frac{1}{x}+\frac{1}{y} = \frac{1}{7}$

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True
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False

Explanation

$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{7}$

$7(x +y) = xy$

$7x + 7y = xy$
The equation

$7x + 7y = xy$ 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.

Express the given information in mathematical form using two variables:

One number is 5 more than seven times the other number.

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$x\, +\, 5y\, =\, 7$
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$7x\, -\, y\, =\, 8$
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$x\, -\, 7y\, =\, 5$
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Insufficient data

Explanation

Let the two numbers be

$'x'$ and

$'y'$ .

Now, according to question

$x=5+(7\times y)$

$\Rightarrow x-7y=5$ , which is a required expression.

Any point on

$y$ axis is of the form

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

Explanation

Any point on

$x$ axis is of the form

$(x,0)$ and any point on

$y$ axis is of the form

$(0,y)$ .

For example,

$(0,5)$ is a point that lies on

$y$ axis.

The equation

$x=7$ can be written in two variables

$x,\,y$ as

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

Explanation

In general, it is obvious that if we want to write an equation

$ax=0$ in terms of two variables then it may be written as

$ax+(0\times y)=0$ .

Hence, the equation

$x=7$ can be written in two variables

$x$ and

$y$ as:

$(1\times x)+(0\times y)=7$

Frame simultaneous linear equations in two variables representing the following information:

Sum of the ages of Monali and Sonali is 29 years. Monali is younger than Sonali by 3 years.

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$x+y=29, \, \, x-y=3$
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$x+y=29, \, \, x-y=-3$
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$x-y=29, \, \, x+y=3$
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None of these

Explanation

Let, the present age of Monali be

$x$ yrs and that of sonali be

$y$ yrs.
As per condition 1 ie., Sum of the ages of Monali and Sonali is 29 years.
The equation becomes,

$x+y=29$
As per condition 2 i.e., Monali is younger than Sonali by 3 years.
The equation becomes,

$x=y-3$

$\therefore x-y=-3$

$y = 2$ is a line

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parallel to $x$ -axis
0%
parallel to $y$ -axis
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passing through origin
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none

Explanation

$\textbf {Hint:Using slope Intercept form }$

$\textbf{Step 1: Find the position of line}$

$\text{ In general, $$x=a$$ is a line parallel to $$y-$$axis ands and $$y=b$$ is a line parallel to $$x$$-axis. }$

$\text{ Hence, $$y=2$$ is a line parallel to x-axis}$

$\text{In other words.}$

$\text{The equation of}$

$y=2$

$\text{is in slope intercept from where the slope is 0 and the y intercept 2 }$

$\text{Hence, the y=2 is a line parallel to x Axis}$

$\textbf{Option A is correct}$

Which equation represents the line that passes through the point

$(-5, -3)$ and is parallel to the

$x$ -axis?

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$x = -5$
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$y = -5$
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$x = -3$
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$y = -3$

Explanation

The graph represents a line that is parallel to the

$x$ -axis and passes through the point

$(-5, -3)$ is

$y = -3$ .

Consider the equation:

$\displaystyle y+7x=3x-2y+28$

If the equation is written in the form of

$\displaystyle ax+by=c$ , then what is the value of a?

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$1$
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$7$
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$3$
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$4$

Explanation

$\displaystyle y+7x=3x-2y+28$

$\displaystyle y+7x-3x+2y=28$

$\displaystyle 4x+3y=28$
Thus, we have

$\displaystyle a=4,b=3,c=28$

Which equation represents the line that passes through the point

$(-2, 3)$ and is parallel to the

$x$ -axis?

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$x = 3$
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$y = 0$
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$x = 0$
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$y = 3$

Explanation

The graph represents a line that is parallel to the

$x$ -axis and passes through the point

$(-2, 3)$ is

$y = 3$ .

Which equation represents the line that passes through the point

$(2, 3)$ and is parallel to the

$y$ -axis?

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$x = 2$
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$y = 3$
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$x = 3$
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$y = 2$

Explanation

The graph represents a line that is parallel to the

$y$ -axis and passes through the point

$(2, 3)$ is

$x = 2.$

Which of the following is a linear equation in

$2$ variables?

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$\displaystyle { x }^{ 2 }+{ y }^{ 2 }=9$
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$\displaystyle { x }^{ 2 }+{ y }^{ 2 }=0$
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$\displaystyle 2x+3=y$
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$\displaystyle x>y$

Explanation

The general form of a linear equation in two variable is

$ax+by+c=0$ where

$x$ and

$y$ are variables and

$a,b,c$ are constants.

Hence, the equation

$2x+3=y$ or

$2x-y=-3$ is a linear equation with two variables

$x$ and

$y$ .

Which equation represents the line that passes through the point

$(1, 3)$ and is parallel to the

$x$ -axis?

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$y = 3$
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$y = 1$
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$x = 1$
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$x = 3$

Explanation

We know that the equation of a line parallel to the x-axis is of the form

$y=b$ where

$b$ is the perpendicular distance of line from the x-axis.

since

$y=b$ passes through the point

$(1, 3)$ .

$\implies$ point

$(1,3)$ lie on the line

$y=b$

since point

$(1,3)$ is at

$3$ units of perpendicular distance from the x-axis

$\implies$ equation is

$y=3$ .

Which equation represents the line that passes through the point

$(0, 3)$ and is parallel to the

$x$ -axis?

0%
$x = 3$
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$y = 0$
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$x = 0$
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$y = 3$

Explanation

General equation of a line which is parallel to

$X$ -axis is of the form

$y=a$ .
Since the line passes through the point

$(0, 3)$ , it's equation is given by

$y = 3$ .

Which equation represents the line that passes through the point

$(2, 1)$ and is parallel to the

$x$ -axis?

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

Explanation

The graph represents a line that is parallel to the

$x$ -axis and passes through the point

$(2, 1)$ is

$y = 1$ .

Identify the linear equation in two variables.

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$2x + 3y = 1$
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$2x^2 - 1 = y$
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$3x^2 + 5 = y^2$
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$6x^3 - 1 = 0$

Explanation

An equation in the form

$ax + by + c = 0$ is called linear equation.

So,

$2x + 3y = 1$ is a linear equation in two variables.

Hence, option A is correct.

Which equation represents the line that passes through the point

$(5, -3)$ and is parallel to the

$y$ -axis?

0%
$x = -3$
0%
$y = -3$
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$x = 5$
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$y = 5$

Which equation represents the line that passes through the point

$(6, 2)$ and is parallel to the

$y$ -axis?

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$y = 6$
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$x = 2$
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$x = 6$
0%
$y = 2$

Explanation

We know that the equation of a line parallel to the y-axis is

$x=a.$

Given: The line passes through the point

$(6, 2)$

Hence the equation of a line that is parallel to the

$y$ -axis and passes through the point

$(6, 2)$ is

$x = 6$

Choose the correct equation that represents the graph above.

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

Explanation

The graph represents a line that is parallel to the

$y$ -axis and passes through the point

$(2, 1)$ is

$x = 2$ .

Which equation represents the line that passes through the point

$(-1, 4)$ and is parallel to the

$y$ -axis?

0%
$y = -1$
0%
$x = -1$
0%
$x = 4$
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$y = 4$

Explanation

The graph represents a line that is parallel to the

$y$ -axis and passes through the point

$(-1, 4)$ is

$x = -1$ .

What is the equation for the graph shown above?

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$y = 2$
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$y = -4$
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$x = 2$
0%
$x = -4$

Explanation

We can observe from the given graph that the line is parallel to the

$y$ -axis and passes through the point

$(-4, 2)$ .

Hence, it represents

$x = -4$ .

Which equation represents the line that passes through the point

$(-5, -4)$ and is parallel to the

$y$ -axis?

0%
$x = -5$
0%
$x = -4$
0%
$y = -5$
0%
$y = -4$

Explanation

Equation of line parallel to

$y-$ axis is of the form

$x=a$

$x-$ co-ordinate of this line remains same throughout. Also it is given that it passes through

$(-5,-4)$ .

Thus required equation of line is

$x=-5$

Identify the equation for the above graph.

0%
$x = 2$
0%
$x = 4$
0%
$y = 4$
0%
$y = 2$

Explanation

The graph represents a line that is parallel to the

$x$ -axis and passes through the point

$(2, 4)$ .

Since it is parallel to x-axis and passes through

$(2,4)$ therefore its equation is

$y = 4$ .

CBSE Questions for Class 9 Maths Linear Equations In Two Variable Quiz 3 - 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 3 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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