MCQ Questions for Class 9 Maths Linear Equations In Two Variable Quiz 2

Write of the following equation in the form

$ax + by + c = 0$ and indicate the values of

$a, b$ and

$c$ .

$2x + 3y = 9.35$

0%
$2x + 3y + (-9.35) = 0$
0%
$2x + 4y + (-9.35) = 0$
0%
$2x + 3y + (-9.25) = 0$
0%
$x + 3y + (-9.35) = 0$

Explanation

The given equation in the form

$ax + by + c = 0$

$\Rightarrow 2x+3y-9.35=0$
Comparing with

$ax+by+c=0$

$\Rightarrow a=2$

$\Rightarrow b=3$

$\Rightarrow c=-9.35$

If we write

$\displaystyle 3x-7y=10$ in form of

$\displaystyle ax+by+c=0,$ then

$b=$ ?

0%
$3$
0%
$7$
0%
$-7$
0%
$10$

Explanation

$3x-7y=10$ can be written as

$3x-7y-10=0$

Now comparing this with

$ax+by+c=0$ we get,

$a=3, b=-7,c=-10$

Linear equation in one variable has

0%
Only constant term.
0%
Only one variable with power $1$ .
0%
Only one term with a variable.
0%
Only one variable with any power.

Explanation

${\textbf{Step-1: Use definition of linear equation in one variable }}$

$\text{Linear equation is in the form ax+b=0 where x is variable and a and b are constants}$

${\text{Example, 5x-10=5 has only one variable.}}$

${\textbf{Hence, answer is an equation one variable raised to the power 1.}}$

Cost of one apple is 3 times the cost of an orange. Write a linear equation for the statement.

0%
$\displaystyle y=3x$
0%
$\displaystyle y=x$
0%
$\displaystyle y=x+3$
0%
$\displaystyle y=x-3$

Explanation

Cost of one apple = y
Cost of one orange = x

$\displaystyle y=3x$

Fill in the blank:
An equation in the form ax + by + c = 0 is called ____________ equation.

0%
Non-linear
0%
Linear
0%
Quadratic
0%
Polynomial

Explanation

An equation in the form

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

The linear equation always forms a straight line when you graph them.

Hence, option B is correct.

If we write

$\displaystyle 3x-7y=10$ in form of

$\displaystyle ax+by+c=0,$ then

$c=$ ?

0%
$3$
0%
$-10$
0%
$7$
0%
$10$

Explanation

$3x-7y=10$ can be written as

$3x-7y-10=0$

Now comparing this with

$ax+by+c=0$ we get,

$a=3, b=-7,c=-10$

Hence option

$C$ s the correct answer

Which of the following is a linear equation?

0%
$2x + y = x + x^{2}$
0%
$5x = 6x + 3y$
0%
$3x + x^{3} - 2y$
0%
$4x - y = y^{2}$

Explanation

Linear equation do not have exponents, square roots.
So, here the linear equation is

$5x = 6x + 3y$

Cost of one apple is 3 times the cost of an orange. This is an example of linear equation in ..... variables.

0%
$0$
0%
$1$
0%
$2$
0%
$3$

Explanation

Cost of one apple

$= y$
Cost of one orange

$= x$

$\displaystyle y=3x$

Since we have two variables

$x$ and

$y$ in our equation, it is a linear equation in two variables.

$\displaystyle 4x+2y=16$

Above equation is linear equation in how many variables?

0%
$1$
0%
$2$
0%
$3$
0%
$0$

Explanation

$\displaystyle \because$ There are two variables

$x$ and

$y$ in the linear equation so, it is a linear equation in

$2$ variables.

The cost of a notebook

$(y)$ is twice that of a pen

$(x)$ .
Write a linear equation to represent this statement.

0%
$\displaystyle y=x+2$
0%
$\displaystyle y=2x$
0%
$\displaystyle y=x$
0%
$\displaystyle y=x-2$

Explanation

Let cost of a notebook is

$y$ and cost of a pen is

$x$ .

Therefore, according to the question,

it is said that cost of a notebook is twice that of a pen.
Thus,

$\displaystyle y=2x$

Consider the equation:

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

How many variables are present in the linear equation?

0%
One
0%
Two
0%
Three
0%
Four

Explanation

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

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

$\displaystyle 4x+3y=28$
Hence, the equation is in

$2$ variables i.e,

$x$ and

$y$ .

In the given equation

$\displaystyle a=\frac { 2 }{ 3 } b+5$
It is linear equation in ....... variables.

0%
$0$
0%
1
0%
2
0%
3

Father's age is

$10$ more than twice age of his son. What is the number of variables if the statement is written in the form of linear equation?

0%
One
0%
Two
0%
Multivariable
0%
Non-linear

Explanation

Let father's age is

$x$ .
Son's age is

$y$

$\displaystyle x=2y+10$

$\therefore$ The equation is in two variable.

The line

$x - 7 = 0$ is

0%
parallel to $y$ -axis.
0%
parallel to $x$ -axis.
0%
passing through the origin.
0%
none of these.

Explanation

$\textbf{Step 1: Find the line where it belongs to.}$

$\text{The given line is }x-7=0$

$\text{So, } x-7=0 \Rightarrow x=7$

$\text{We know that any line of the form }x=a \text{ is a straight line parallel to the y-axis.}$

$\text{Therefore , the given line }x=7 \text{ is a straight line parallel to the y-axis.}$

$\textbf{Hence, the correct option is A. }$

Which of the following is not a linear equation?

0%
$4x - 3 = 2y + \dfrac{1}{4}$
0%
$3x - y = 13$
0%
$3x + \sqrt{y}^{3} = 0$
0%
$3y = x + 9$

Explanation

The linear equation does not have exponents or any square roots.
So,

$3x + \sqrt{y}^{3} = 0$ is not a linear equation.

Choose the option which is not a linear equation.

0%
$3x - y = 12$
0%
$3y - x + 2 = x + 2y$
0%
$3x - 6y = 0$
0%
$3x^{2}-y^{4}= 12 - x^{2}$

Explanation

Linear equation do not have exponents, square roots.
So,

$3x^{2}-y^{4}= 12 - x^{2}$ is not a linear equation.

Gopaiah sowed wheat and paddy in two fields of total area

$5000$ square meters. Write a linear equation

0%
$x + y = 5000$
0%
$x - y = 5000$
0%
$x + y+5000=0$
0%
None of these

Explanation

In the question it is not given that how much paddy and wheat are sown areawise, separately.

so, let us assume that paddy is sown in an area of

$x$ square metres,

and wheat is sown in an area of

$y$ square metres,

According to question,

Total area is

$5000$ square metres

so, equation would be

$x+y=5000$

Which of the following is not a linear equation?

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

Explanation

$C$ is not a linear equation because it consists

${y}^{2}$ in it. Linear equation will not contain any exponent to variables

The cost of a note book is twice the cost of a pen. If the cost of a note book is

$'x'$ and that of a pen is

$'y'$ then a linear equation in two variables to represent the given condition is ____.

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

Explanation

Cost of notebook

$=x$

Cost of pen

$=y$

Given that, the cost of a notebook is twice as that of a pen.

$\therefore x=2y$

$\Rightarrow x-2y=0$

The graph of the linear equation

$y=x$ passes through the point

0%
$(\dfrac{3}{2},-\dfrac{3}{2})$
0%
$(0,\dfrac{3}{2})$
0%
$(1,1)$
0%
$(-\dfrac{1}{2},\dfrac{1}{2})$

Explanation

$y=x$ is a linear equation , means the value of

$y$ is same as value of

$x$ .

Thus checking in options :

when

$x=1,$ then

$y=1$ is the only option where the value of

$y=x$ .

Hence option C is correct.

The equation

$\sqrt{a^{2} + b^{2}} =a+b$ is a linear equation in 2 variables

0%
True
0%
False

Explanation

$\sqrt{a^2 + b^2} = a + b$

squaring on both sides we get,

$a^2 + b^2 = (a + b)^2$

$a^2 + b^2 = a^2 + b^2 + 2ab$

$2ab = 0$

which is not in the form of

$ax + by + c = 0$

So, the given statement is False.

The total cost of

$2$ shirts and

$3$ pants is

$Rs.1000.$ Which of the following equation represent the above statement ?

0%
$2x-3y=1000$
0%
$2x+3y=1000$
0%
$2x-3y+1000=0$
0%
$3x-2y=1000$

Explanation

Suppose Cost of one shirt is

$x$

So cost of two shirts will be

$2x$

Let cost of one pant be

$y$

So cost of three pants will be

$3y$

Total Cost

$=1000$

$\Rightarrow 2x+3y=1000$ Ans.

If a linear equation has solutions

$(-2,2), (0,0)$ and

$(2, -2),$ then it is of the form

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

Explanation

The points

$(-2,2)$ and

$(2,-2)$ have

$x$ and

$y$ coordinated of opposite signs.
Also, any point on the graph of

$x$ +

$y$ =

$0$
i.e.,

$y = -x$ will have

$x$ and

$y$ coordinate of opposite signs. The point

$(0,0)$ also satisfies

$x + y = 0.$
Hence,

$(b)$ is the correct answer.

The graph of

$y = 6$ is a line

0%
parallel to x -axis at a distance $6$ units from the origin
0%
parallel to y -axis at a distance $6$ units from the origin
0%
making an intercept $6$ on the x-axis.
0%
making an intercept $6$ on both the axes.

Explanation

The given equation

$y = 6$ does not contain

$x.$ Its graph is a line parallel to

$x-$ axis.
So, the graph of

$y = 6$ is a line parallel to

$x-$ axis at a distance

$6$ units from the origin.
Hence,

$(a)$ is the correct answer.

The graph given below represents the linear equation

$x + y= 0.$

0%
True
0%
False

Explanation

The given equation is

$x + y = 0,$ i.e.,

$y = -x.$
Any point on the graph of

$y -x,$ will have

$x$ and

$y$ coordinated of opposite signs.
As the points

$(-1,1)$ and

$(-3,3)$ have

$x$ and

$y$ coordinated of opposite signs, so these points satisfy the given equation and the two points determine a unique line, hence the given statement is true.

The graph of

$y = 6$ is a line

0%
parallel to $x-$ axis & at a distance of $6$ units from the $x-$ axis.
0%
parallel to $y-$ axis at a distance of $6$ units from the origin.
0%
making an intercept $6$ on the $x-$ axis.
0%
making an intercept $6$ on both the axes.

Explanation

The given equation is

$y=6$
We can write it as

$y=0.x+6$
i.e. for every value of

$x$ , we have

$y=6$
So, the points are

$(0,6),(-1,6), (1,6), (3,6)....$
On plotting these points, we get a straight line parallel to the

$x-$ axis at a distance of

$6$ units from the

$x-$ axis.

A class has total

$60$ students with

$x$ girls and

$y$ boys. The number of girls is twice the number of boys. Express these statement in the linear equations form.

0%
$x+y=60,$ $x=2y$
0%
$x-y=60,$ $x=2y$
0%
$x+y=60,$ $x=3y$
0%
None of these

Explanation

Given: Total number of students (i.e, boys

$(y)$ and girls

$(x)$ ) in the class is

$60$ .

Therefore,

$x+y=60$

And number of girls is twice the number of boys, so

$x = 2y$

Hence option

$A$ is correct choice

State true or false:

The graph given below represents the linear equation

$x = 3$

0%
True
0%
False

Explanation

From the graph, it is clear that the given line is parallel to the y-axis and at a distance of 3 units from the y-axis.
Also, each point on the line is of the form

$(3,a)$ i.e.

$x=3$ , and

$y$ can have any real value.
So, the equation of line is

$x=3$ .

State true or false:

The point

$(0, 3)$ lies on the graph of the linear equation

$3x + 4y = 12.$

0%
True
0%
False

Explanation

If the point

$(0,3)$ lies on the graph of the linear equation

$3x+4y=12$ ,

the co-ordinates of the point should satisfy the equation.

Therefore, LHS

$= 3\left( 0 \right) +4\left( 3 \right)$

$\Rightarrow 0+12=12 =$ RHS

$\therefore$ LHS

$=$ RHS

Answer is True.

Which of the following represent a line parallel to

$x$ -axis?

0%
$x + y = 3$
0%
$2x + 3 = 7$
0%
$2 -y- 3= y +1$
0%
$x + 3 = 0$

Explanation

Any straight line parallel to

x−x−axis is given by

y=k,y=k, where

kk is the distance of the line from

x−x−axis.

In option C, we have

$2-y-3 = y+1$

$\implies y = -1$ .

CBSE Questions for Class 9 Maths Linear Equations In Two Variable Quiz 2 - 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 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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