Linear Equations in Two Variables Test

Result

Linear Equations in Two Variables Test - 22

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The graph of the linear equation $$y=x$$ passes through the point

A
$$(\dfrac{3}{2},-\dfrac{3}{2})$$

B
$$(0,\dfrac{3}{2})$$

C
$$(1,1)$$

D
$$(-\dfrac{1}{2},\dfrac{1}{2})$$

Solution

As $$ y=x$$ 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.
Question 2
1 / -0

The total cost of $$2$$ shirts and $$3$$ pants is $$Rs.1000.$$ Which of the following equation represent the above statement ?

A
$$2x-3y=1000$$

B
$$2x+3y=1000$$

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

D
$$3x-2y=1000$$

Solution

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.
Question 3
1 / -0

If a linear equation has solutions $$(-2,2), (0,0)$$ and $$(2, -2),$$ then it is of the form

A
$$y - x = 0$$

B
$$x + y = 0$$

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

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

Solution

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.
Question 4
1 / -0

The graph of $$y = 6$$ is a line

A
parallel to x -axis at a distance $$6$$ units from the origin

B
parallel to y -axis at a distance $$6$$ units from the origin

C
making an intercept $$6$$ on the x-axis.

D
making an intercept $$6$$ on both the axes.

Solution

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.
Question 5
1 / -0

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

A
$$x=3y-1$$

B
$$y=2x+3$$

C
$$x^2 - 5 =0$$

D
$$x-y =0$$

Solution

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 $$2$$.
Question 6
1 / -0

Draw the graphs of linear equations $$y = x$$ and $$y =- x$$ on the same cartesian plane. What do you observe?

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

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

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

D
Graph of each equation is a line passing through $$(1, 0)$$.
Question 7
1 / -0

Which of the following represent a line parallel to $$x$$-axis?

A
$$x + y = 3$$

B
$$2x + 3 = 7$$

C
$$2 -y- 3= y +1$$

D
$$x + 3 = 0$$

Solution

Any straight line parallel to x−axis is given by y=k, where k is the distance of the line from x−axis.
In option C, we have
$$2-y-3 = y+1$$
$$\implies y = -1$$.
Question 8
1 / -0

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.

A
$$x+y=10, x=4y$$

B
$$x-y=10, x=4y$$

C
$$xy=10, x+4y=0$$

D
None of these

Solution

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
Question 9
1 / -0

Graph of linear equation $$4x = 5$$ in a plane is:

A
Parallel to $$x -axis$$

B
Parallel to $$y- axis$$

C
Lies along $$x - axis$$

D
Passes through origin

Solution

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.
Question 10
1 / -0

The graph of $$y = 6$$ is a line

A
parallel to $$x-$$axis & at a distance of $$6$$ units from the $$x-$$axis.

B
parallel to $$y-$$axis at a distance of $$6$$ units from the origin.

C
making an intercept $$6$$ on the $$x-$$axis.

D
making an intercept $$6$$ on both the axes.

Solution

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.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Linear Equations in Two Variables Test - 22

Result

Linear Equations in Two Variables Test - 22

Score

-

Rank

-

SHARING IS CARING

Question 1

$$(\dfrac{3}{2},-\dfrac{3}{2})$$

$$(0,\dfrac{3}{2})$$

$$(1,1)$$

$$(-\dfrac{1}{2},\dfrac{1}{2})$$

Solution

Question 2

$$2x-3y=1000$$

$$2x+3y=1000$$

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

$$3x-2y=1000$$

Solution

Question 3

$$y - x = 0$$

$$x + y = 0$$

$$-2x + y = 0$$

$$-x + 2y = 0$$

Solution

Question 4

parallel to x -axis at a distance $$6$$ units from the origin

parallel to y -axis at a distance $$6$$ units from the origin

making an intercept $$6$$ on the x-axis.

making an intercept $$6$$ on both the axes.

Solution

Question 5

$$x=3y-1$$

$$y=2x+3$$

$$x^2 - 5 =0$$

$$x-y =0$$

Solution

Question 6

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

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

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

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

Question 7

$$x + y = 3$$

$$2x + 3 = 7$$

$$2 -y- 3= y +1$$

$$x + 3 = 0$$

Solution

Question 8

$$x+y=10, x=4y$$

$$x-y=10, x=4y$$

$$xy=10, x+4y=0$$

None of these

Solution

Question 9

Parallel to $$x -axis$$

Parallel to $$y- axis$$

Lies along $$x - axis$$

Passes through origin

Solution

Question 10

parallel to $$x-$$axis & at a distance of $$6$$ units from the $$x-$$axis.

parallel to $$y-$$axis at a distance of $$6$$ units from the origin.

making an intercept $$6$$ on the $$x-$$axis.

making an intercept $$6$$ on both the axes.

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.