Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 17

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Question 1
1 / -0

How many linear equations in $$x$$ and $$y$$ can be satisfied by $$x = 1$$ and $$y = 2$$?

A
Only one

B
Two

C
Infinitely many

D
Three

Solution

From the graph, its clear that infinite straight lines can pass through the point (1,2).
So, infinite linear equation are possible satisfying $$x=1,y=2$$
Question 2
1 / -0

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

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

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

C
$$a = 0, b = 0$$

D
$$a \neq 0, b \neq 0$$

Solution

The condition for $$ax+by+c=0$$ to be a linear eqaution in two variables is
$$ a\neq 0\quad , b\neq 0 $$
Question 3
1 / -0

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

A
$$1.x + 5 = 10$$

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

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

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

Solution

$$x=5$$
$$\Rightarrow$$ $$ x-5=0$$
$$\Rightarrow$$ $$ 1.x+(-5)=0$$
$$\Rightarrow$$ $$ 1.x+0.y+(-5)=0$$
Question 4
1 / -0

Linear equation in one variable is :

A
$$2x = y$$

B
$$y^2 = 3y + 5$$

C
$$4x - y = 5$$

D
$$3t + 5 = 9t- 7$$

Solution

A linear equation with one variable is an equation with only one variable and the highest power of the variable is $$1$$.

In first option, there are $$2$$ variables, $$x$$ and $$y$$.

In the second option, there is only a $$1$$ variable but the highest power is $$2$$ hence, it is a quadratic equation.

In the third option, there are $$2$$ variables, $$x$$ and $$y$$.

In the fourth option, there is only $$1$$ variable and the highest power is $$1$$ as well.

Hence, option $$D$$ is correct,
Question 5
1 / -0

Age of $$x$$ exceeds the age of $$y$$ by 7yrs. This statement can be expressed as the linear equation as :

A
$$x + y + 7 = 0$$

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

C
$$x - y - 7 = 0$$

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

Solution

According to question,
$$x-y=7$$
$$\Rightarrow$$ $$x-y-7=0$$
So, option C is correct.
Question 6
1 / -0

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

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

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

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

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

Solution

$$x =7$$ can be written as, $$1.x + 0.y =7 $$ as the coefficient of $$x$$ is $$1$$ and that of $$y $$ is $$0$$.
Question 7
1 / -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.

A
$$(i)$$ 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.

B
$$(i)$$ 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.

C
$$(i)$$ 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.

D
$$(i)$$ 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.

Solution

By plotting the points on the graph, we get a line $$x=2$$ which is parallel to $$y-$$axis.
Question 8
1 / -0

Which of the following equation represents a straight line which is parallel to the $$x$$-axis and at a distance $$3$$ units below it?

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

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

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

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

Solution

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 $$y=-3$$.
Question 9
1 / -0

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

A
$$y$$ axis

B
$$x$$ axis

C
$$y=x$$

D
$$y=2x$$

Solution

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.
Question 10
1 / -0

Is the following equation linear in two variables?
$$\displaystyle \frac{4}{x} + 3y = 14$$

A
Yes

B
No

C
Ambiguous

D
Data Insufficient

Solution

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

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Re-Attempt Weekly Quiz Competition

Linear Equations in Two Variables Test - 17

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Linear Equations in Two Variables Test - 17

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Question 1

Only one

Two

Infinitely many

Three

Solution

Question 2

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

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

$$a = 0, b = 0$$

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

Solution

Question 3

$$1.x + 5 = 10$$

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

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

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

Solution

Question 4

$$2x = y$$

$$y^2 = 3y + 5$$

$$4x - y = 5$$

$$3t + 5 = 9t- 7$$

Solution

Question 5

$$x + y + 7 = 0$$

$$x - y + 7 = 0$$

$$x - y - 7 = 0$$

$$x + y - 7 = 0$$

Solution

Question 6

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

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

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

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

Solution

Question 7

$$(i)$$ 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.

$$(i)$$ 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.

$$(i)$$ 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.

$$(i)$$ 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.

Solution

Question 8

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

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

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

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

Solution

Question 9

$$y$$ axis

$$x$$ axis

$$y=x$$

$$y=2x$$

Solution

Question 10

Yes

No

Ambiguous

Data Insufficient

Solution

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$$(i)$$ 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.

$$(i)$$ 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.

$$(i)$$ 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.

$$(i)$$ 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.