Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Write the following equations in the form ax + by + c = 0
$$x - 4 = \sqrt 3 y$$

A
$$x + (- \sqrt 3)y + (-4) = 0$$

B
$$x + ( \sqrt 3)y + (-4) = 0$$

C
$$x + (- \sqrt 3)y + (4) = 0$$

D
$$2x + (- \sqrt 3)y + (-4) = 0$$

Solution

The given equation in the form $$ax + by + c = 0 $$
$$\Rightarrow x-\sqrt{3}y-4=0$$
Comparing with $$ax+by+c=0$$
$$\Rightarrow a=1$$
$$\Rightarrow b=-\sqrt{3}$$
$$\Rightarrow c=-4$$
Question 2
1 / -0

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

A
$$(x,y)$$

B
$$(0,y)$$

C
$$(0,0)$$

D
$$(x,0)$$

Solution

$$\textbf{Step 1: Writing Coordinates of given point}$$
$$\text{We know that any point on the x-axis}\implies y=0$$
$$\text{Hence, any point on the x-axis can be expressed as (x,0)}$$
$$\textbf{Hence, Any point on the x-axis can be expressed as of the form (x,0)}$$
Question 3
1 / -0

Write the following equation in the form of $$ax + by + c = 0$$.
$$5x - 3y = 4$$

A
$$5x + (-3)y + (-4) = 0$$

B
$$5x + (3)y + (-4) = 0$$

C
$$5x + (-3)y + (4) = 0$$

D
$$4x + (-3)y + (4) = 0$$

Solution

The given equation in the form $$ax + by + c = 0 $$ is
$$\ 5x-3y-4=0$$
Comparing with $$ax+by+c=0$$
$$\Rightarrow a=5$$
$$\Rightarrow b=-3$$
$$\Rightarrow c=-4$$
Question 4
1 / -0

Write the following equations in the form $$ax + by + c = 0 $$, where $$a= -2,b=3$$ and $$c=-6$$

A
$$-2x +3y -6 = 0$$

B
$$x -3y + 6 = 0$$

C
$$2x + 3y - 6 = 0$$

D
$$2x + 3y + 6 = 0$$

Solution

The given equation in the form $$ax + by + c = 0 $$
$$\Rightarrow -2x+3y-6=0$$
Question 5
1 / -0

What is a linear equation in $$2$$ variables?

A
An equation containing $$2$$ variables raised to the power $$1$$

B
An equation in which the variables are power $$2$$

C
An expression containing $$2$$ variables

D
None of the above

Solution

An equation which has two variables and highest power of the variables is $$1$$ is called a linear equation in 2 variables.
i.e An equation containing 2 variables raised to the power is a linear equation in 2 variables.
Hence, option A is correct.
Question 6
1 / -0

Write the equation $$2x = y$$ in the form of $$ax + by + c = 0:$$

A
$$2x + (-1)y + 0 = 0$$

B
$$2x + (1)y + 0 = 0$$

C
$$2x + (-1)y + 1 = 0$$

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

Solution

The given equation in the form $$ax + by + c = 0 $$ is
$$2x-y+0=0$$
Comparing with $$ax+by+c=0$$
We have
$$ a=2$$
$$ b=-1$$
$$ c=0$$
Question 7
1 / -0

Is $$5x -3y = 5$$ a linear equation in one variable?

A
Yes

B
No

C
Ambiguous

D
Data insufficient

Solution

No, the given equation $$5x - 3y = 5$$ is a linear equation in two variable having $$x$$ and $$y$$ as the two variables.
Question 8
1 / -0

Write of the following equation in the form $$ax + by + c = 0$$ and indicate the values of $$a, b $$ and $$c$$.
$$2x + 3y = 9.35$$

A
$$2x + 3y + (-9.35) = 0$$

B
$$2x + 4y + (-9.35) = 0$$

C
$$2x + 3y + (-9.25) = 0$$

D
$$x + 3y + (-9.35) = 0$$

Solution

The given equation in the form $$ax + by + c = 0 $$
$$\Rightarrow 2x+3y-9.35=0$$
Comparing with $$ax+by+c=0$$
$$\Rightarrow a=2$$
$$\Rightarrow b=3$$
$$\Rightarrow c=-9.35$$
Question 9
1 / -0

If we write $$\displaystyle 3x-7y=10$$ in form of $$\displaystyle ax+by+c=0,$$ then $$b=$$?

A
$$3$$

B
$$7$$

C
$$-7$$

D
$$10$$

Solution

$$3x-7y=10$$ can be written as $$3x-7y-10=0$$
Now comparing this with $$ax+by+c=0$$ we get,
$$a=3, b=-7,c=-10$$
Question 10
1 / -0

Linear equation in one variable has

A
Only constant term.

B
Only one variable with power $$1$$.

C
Only one term with a variable.

D
Only one variable with any power.

Solution

$${\textbf{Step-1: Use definition of linear equation in one variable }}$$
$$\text{Linear equation is in the form ax+b=0 where x is variable and a and b are constants}$$
$${\text{Example, 5x-10=5 has only one variable.}}$$
$${\textbf{Hence, answer is an equation one variable raised to the power 1.}}$$

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Re-Attempt Weekly Quiz Competition

Linear Equations in Two Variables Test - 19

Result

Linear Equations in Two Variables Test - 19

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SHARING IS CARING

Question 1

$$x + (- \sqrt 3)y + (-4) = 0$$

$$x + ( \sqrt 3)y + (-4) = 0$$

$$x + (- \sqrt 3)y + (4) = 0$$

$$2x + (- \sqrt 3)y + (-4) = 0$$

Solution

Question 2

$$(x,y)$$

$$(0,y)$$

$$(0,0)$$

$$(x,0)$$

Solution

Question 3

$$5x + (-3)y + (-4) = 0$$

$$5x + (3)y + (-4) = 0$$

$$5x + (-3)y + (4) = 0$$

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

Solution

Question 4

$$-2x +3y -6 = 0$$

$$x -3y + 6 = 0$$

$$2x + 3y - 6 = 0$$

$$2x + 3y + 6 = 0$$

Solution

Question 5

An equation containing $$2$$ variables raised to the power $$1$$

An equation in which the variables are power $$2$$

An expression containing $$2$$ variables

None of the above

Solution

Question 6

$$2x + (-1)y + 0 = 0$$

$$2x + (1)y + 0 = 0$$

$$2x + (-1)y + 1 = 0$$

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

Solution

Question 7

Yes

No

Ambiguous

Data insufficient

Solution

Question 8

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

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

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

$$x + 3y + (-9.35) = 0$$

Solution

Question 9

$$3$$

$$7$$

$$-7$$

$$10$$

Solution

Question 10

Only constant term.

Only one variable with power $$1$$.

Only one term with a variable.

Only one variable with any power.

Solution

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