Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

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.

A
$$2x\, +\, 5y\, =\, 2200$$

B
$$x\, +\, 10y\, =\, 800$$

C
$$10x\, -\, 5y\, =\, 1800$$

D
Insufficient data

Solution

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.
Question 2
1 / -0

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

A
$$x + 6 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

B
$$x + 16 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

C
$$x - 6 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

D
$$x + 6 = 2y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin
Question 3
1 / -0

A straight line parallel to the $$x$$-axis has equation

A
$$x = a$$

B
$$y = a$$

C
$$y = x$$

D
$$y = -x$$

Solution

A straight line parallel to the $$x$$ axis has equation $$ y=a$$.
Question 4
1 / -0

The graph of the equation $$x= b$$ is also a straight line parallel to _____.

A
$$y$$-axis

B
$$x$$-axis

C
Cannot be determined

D
Not Parallel

Solution

The graph of the equation x = b is always a straight line parallel to y-axis.
Question 5
1 / -0

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

A
$$ 2x + 0y + 3 = 0$$

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

C
$$ 2x + 2y + 3 = 0$$

D
$$ 3x + 0y + 3 = 0$$

Solution

The given equation
$$2x = -3$$
It can be written as
$$2.x + 0.y = -3$$
$$\Rightarrow 2.x + 0.y + 3 = 0$$
Question 6
1 / -0

Write a linear equation in two variables to represent each of the following statement.
5 books and 7 pens together cost Rs 79.

A
5x + 7y = 79, where x = cost of a book and y = cost of a pen.

B
4x + 7y = 79, where x = cost of a book and y = cost of a pen.

C
5x + 6y = 79, where x = cost of a book and y = cost of a pen.

D
5x - 7y = 79, where x = cost of a book and y = cost of a pen.

Solution

The cost of 1 book$$=x$$
The cost of 1 pen$$=y$$
Then the linear equation is $$\Rightarrow 5x+7y=79$$
Question 7
1 / -0

Write the following equation as an equation in two variables:
$$3y = 4$$

A
$$0x + 3y - 4 = 0$$

B
$$0x + 2y - 4 = 0$$

C
$$0x + 3y - 5 = 0$$

D
$$2x + 3y - 4 = 0$$

Solution

The given equation is $$3y = 4$$
This can be written as $$0.x + 3.y = 4$$ $$\Rightarrow 0x + 3y - 4 = 0$$
Question 8
1 / -0

The graph of the equation $$y = a$$ is a straight line parallel to _____

A
$$x$$-axis

B
$$y$$-axis

C
Cannot be determined

D
Not Parallel

Solution

The graph of the equation y = a is always a straight line parallel to x-axis.
Question 9
1 / -0

Write a linear equation in two variables to represent the following statement.
The cost of a pen is thrice the cost of a pencil

A
$$x = 3y,$$ where $$x =$$ cost of a pen and $$y =$$ cost of a pencil.

B
$$x = 2y,$$ where $$x =$$ cost of a pen and $$y =$$ cost of a pencil.

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

D
$$x = y$$, where $$x =$$ cost of a pen and $$y =$$ cost of a pencil.

Solution

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
Question 10
1 / -0

Which of the following equation is not a linear equation?

A
$$2x + 3 = 7x - 2$$

B
$$\displaystyle \frac{2}{3}x + 5 = 3x - 4$$

C
$$\displaystyle x^2 + 3 = 5x - 3$$

D
$$\displaystyle (x - 2)^2 = x^2 + 8$$

Solution

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.

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Re-Attempt Weekly Quiz Competition

Linear Equations in Two Variables Test - 18

Result

Linear Equations in Two Variables Test - 18

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SHARING IS CARING

Question 1

$$2x\, +\, 5y\, =\, 2200$$

$$x\, +\, 10y\, =\, 800$$

$$10x\, -\, 5y\, =\, 1800$$

Insufficient data

Solution

Question 2

$$x + 6 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

$$x + 16 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

$$x - 6 = y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

$$x + 6 = 2y$$, where $$x =$$ age of Jenson and $$y =$$ age of Gibin

Question 3

$$x = a$$

$$y = a$$

$$y = x$$

$$y = -x$$

Solution

Question 4

$$y$$-axis

$$x$$-axis

Cannot be determined

Not Parallel

Solution

Question 5

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

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

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

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

Solution

Question 6

5x + 7y = 79, where x = cost of a book and y = cost of a pen.

4x + 7y = 79, where x = cost of a book and y = cost of a pen.

5x + 6y = 79, where x = cost of a book and y = cost of a pen.

5x - 7y = 79, where x = cost of a book and y = cost of a pen.

Solution

Question 7

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

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

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

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

Solution

Question 8

$$x$$-axis

$$y$$-axis

Cannot be determined

Not Parallel

Solution

Question 9

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

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

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

$$x = y$$, where $$x =$$ cost of a pen and $$y =$$ cost of a pencil.

Solution

Question 10

$$2x + 3 = 7x - 2$$

$$\displaystyle \frac{2}{3}x + 5 = 3x - 4$$

$$\displaystyle x^2 + 3 = 5x - 3$$

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

Solution

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