Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

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.

A
$$x+y=60,$$ $$x=2y$$

B
$$x-y=60,$$ $$x=2y$$

C
$$x+y=60,$$ $$x=3y$$

D
None of these

Solution

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
Question 2
1 / -0

Draw the graph for the linear equation $$3y+5=0$$ and select the correct option:

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

B
The line is parallel to the $$y$$-axis and passes through $$\left (0, -\dfrac53\right)$$

C
The line is parallel to the $$x$$-axis and passes through $$\left (0, \dfrac53\right)$$

D
The line is parallel to the $$y$$-axis and passes through $$\left (0, \dfrac53\right)$$
Question 3
1 / -0

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.

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

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

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

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

Solution

Let runs scored by India $$=x$$
Runs scored by Sri lanka $$=y$$

given $$x+y = 679$$

Then the linear equation representing the given statement $$\Rightarrow x+y=679$$
Question 4
1 / -0

Express the given information in mathematical form using two variables:
One number is 5 more than seven times the other number.

A
$$x\, +\, 5y\, =\, 7$$

B
$$7x\, -\, y\, =\, 8$$

C
$$x\, -\, 7y\, =\, 5$$

D
Insufficient data

Solution

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.
Question 5
1 / -0

Any point on $$y$$ axis is of the form

A
$$(x,y)$$

B
$$(0,y)$$

C
$$(y,y)$$

D
$$(x,0)$$

Solution

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.
Question 6
1 / -0

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

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:
$$(1\times x)+(0\times y)=7$$
Question 7
1 / -0

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.

A
$$x+y=29, \, \, x-y=3$$

B
$$x+y=29, \, \, x-y=-3$$

C
$$x-y=29, \, \, x+y=3$$

D
None of these

Solution

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,
$$x=y-3$$
$$\therefore x-y=-3$$
Question 8
1 / -0

$$y = 2$$ is a line

A
parallel to $$x$$-axis

B
parallel to $$y$$-axis

C
passing through origin

D
none

Solution

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

$$\textbf{Step 1: Find the position of line}$$
$$\text{ In general, $$x=a$$ is a line parallel to $$y-$$axis ands and $$y=b$$ is a line parallel to $$x$$-axis. }$$
$$\text{ Hence, $$y=2$$ is a line parallel to x-axis}$$
$$\text{In other words.}$$
$$\text{The equation of}$$ $$y=2$$ $$\text{is in slope intercept from where the slope is 0 and the y intercept 2 }$$
$$\text{Hence, the y=2 is a line parallel to x Axis}$$
$$\textbf{Option A is correct}$$
Question 9
1 / -0

Which equation represents the line that passes through the point $$(-5, -3)$$ and is parallel to the $$x$$-axis?

A
$$x = -5$$

B
$$y = -5$$

C
$$x = -3$$

D
$$y = -3$$

Solution

The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(-5, -3)$$ is $$y = -3$$.
Question 10
1 / -0

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?

A
$$1$$

B
$$7$$

C
$$3$$

D
$$4$$

Solution

$$\displaystyle y+7x=3x-2y+28$$
$$\displaystyle y+7x-3x+2y=28$$
$$\displaystyle 4x+3y=28$$
Thus, we have
$$\displaystyle a=4,b=3,c=28$$

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Linear Equations in Two Variables Test - 23

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Linear Equations in Two Variables Test - 23

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Question 1

$$x+y=60,$$ $$x=2y$$

$$x-y=60,$$ $$x=2y$$

$$x+y=60,$$ $$x=3y$$

None of these

Solution

Question 2

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

The line is parallel to the $$y$$-axis and passes through $$\left (0, -\dfrac53\right)$$

The line is parallel to the $$x$$-axis and passes through $$\left (0, \dfrac53\right)$$

The line is parallel to the $$y$$-axis and passes through $$\left (0, \dfrac53\right)$$

Question 3

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

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

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

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

Solution

Question 4

$$x\, +\, 5y\, =\, 7$$

$$7x\, -\, y\, =\, 8$$

$$x\, -\, 7y\, =\, 5$$

Insufficient data

Solution

Question 5

$$(x,y)$$

$$(0,y)$$

$$(y,y)$$

$$(x,0)$$

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

$$x+y=29, \, \, x-y=3$$

$$x+y=29, \, \, x-y=-3$$

$$x-y=29, \, \, x+y=3$$

None of these

Solution

Question 8

parallel to $$x$$-axis

parallel to $$y$$-axis

passing through origin

none

Solution

Question 9

$$x = -5$$

$$y = -5$$

$$x = -3$$

$$y = -3$$

Solution

Question 10

$$1$$

$$7$$

$$3$$

$$4$$

Solution

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