Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a linear equation?

A
$$y - 3 =\dfrac{1}{4}(x - 2)$$

B
$$y + 2 = x^{3}$$

C
$$3\sqrt{x} - y = 6$$

D
$$x + y^{4} = 0$$

Solution

Linear equations have exponents of the variable equal to $$1.$$
Hence, option $$A$$ is correct.
Question 2
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The line $$x - 7 = 0$$ is

A
parallel to $$y$$-axis.

B
parallel to $$x$$-axis.

C
passing through the origin.

D
none of these.

Solution

$$\textbf{Step 1: Find the line where it belongs to.}$$

$$\text{The given line is }x-7=0$$

$$\text{So, } x-7=0 \Rightarrow x=7$$

$$\text{We know that any line of the form }x=a \text{ is a straight line parallel to the y-axis.}$$

$$\text{Therefore , the given line }x=7 \text{ is a straight line parallel to the y-axis.}$$

$$\textbf{Hence, the correct option is A. }$$
Question 3
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Which of the following is a linear equation?

A
$$y - 2 = 3(x + 1)$$

B
$$x + y^{3} = 1$$

C
$$3x - y = x^{2}$$

D
$$2x - y^{3} = 2$$

Solution

Linear equation do not have exponents, square roots.
So, here the linear equation is $$y - 2 = 3(x + 1)$$
Question 4
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Which of the following is not a linear equation?

A
$$4x - 3 = 2y + \dfrac{1}{4}$$

B
$$3x - y = 13$$

C
$$3x + \sqrt{y}^{3} = 0$$

D
$$3y = x + 9$$

Solution

The linear equation does not have exponents or any square roots.
So, $$3x + \sqrt{y}^{3} = 0$$ is not a linear equation.
Question 5
1 / -0

Choose the option which is not a linear equation.

A
$$3x - y = 12$$

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

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

D
$$3x^{2}-y^{4}= 12 - x^{2}$$

Solution

Linear equation do not have exponents, square roots.
So, $$3x^{2}-y^{4}= 12 - x^{2}$$ is not a linear equation.
Question 6
1 / -0

Which of the following is not a linear equation?

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

B
$$\dfrac{x}{2} + y^{3} = 12$$

C
$$2x = y + 10$$

D
$$x - y = 12 + y$$

Solution

Linear equation do not have exponents, square roots.
So, $$\dfrac{x}{2} + y^{3} = 12$$ is not a linear equation.
Question 7
1 / -0

Which of the following is not a linear equation?

A
$$3x - y + 14 = 24$$

B
$$2x - y = 0$$

C
$$3x + 2p = q + x$$

D
$$x^{3} + y^{3} = 13$$

Solution

Linear equation do not have exponents, square roots.
So, $$x^{3} + y^{3} = 13$$ is not a linear equation.
Question 8
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Gopaiah sowed wheat and paddy in two fields of total area $$5000$$ square meters. Write a linear equation

A
$$x + y = 5000$$

B
$$x - y = 5000$$

C
$$x + y+5000=0$$

D
None of these

Solution

In the question it is not given that how much paddy and wheat are sown areawise, separately.
so, let us assume that paddy is sown in an area of $$x$$ square metres,
and wheat is sown in an area of $$y$$ square metres,
According to question,
Total area is $$5000$$ square metres
so, equation would be
$$x+y=5000$$
Question 9
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Which of the following is not a linear equation?

A
$$5+4x=y+3$$

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

C
$$3-x={y}^{2}+4$$

D
$$x+y=0$$

Solution

$$C$$ is not a linear equation because it consists $${y}^{2}$$ in it. Linear equation will not contain any exponent to variables
Question 10
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The cost of a note book is twice the cost of a pen. If the cost of a note book is $$'x'$$ and that of a pen is $$'y'$$ then a linear equation in two variables to represent the given condition is ____.

A
$$x + 2y = 0$$

B
$$x - 2y = 0$$

C
$$2x + y = 0$$

D
$$2x - y = 0$$

Solution

Cost of notebook $$=x$$
Cost of pen $$=y$$

Given that, the cost of a notebook is twice as that of a pen.
$$\therefore x=2y$$
$$\Rightarrow x-2y=0$$

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Re-Attempt Weekly Quiz Competition

Linear Equations in Two Variables Test - 21

Result

Linear Equations in Two Variables Test - 21

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SHARING IS CARING

Question 1

$$y - 3 =\dfrac{1}{4}(x - 2)$$

$$y + 2 = x^{3}$$

$$3\sqrt{x} - y = 6$$

$$x + y^{4} = 0$$

Solution

Question 2

parallel to $$y$$-axis.

parallel to $$x$$-axis.

passing through the origin.

none of these.

Solution

Question 3

$$y - 2 = 3(x + 1)$$

$$x + y^{3} = 1$$

$$3x - y = x^{2}$$

$$2x - y^{3} = 2$$

Solution

Question 4

$$4x - 3 = 2y + \dfrac{1}{4}$$

$$3x - y = 13$$

$$3x + \sqrt{y}^{3} = 0$$

$$3y = x + 9$$

Solution

Question 5

$$3x - y = 12$$

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

$$3x - 6y = 0$$

$$3x^{2}-y^{4}= 12 - x^{2}$$

Solution

Question 6

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

$$\dfrac{x}{2} + y^{3} = 12$$

$$2x = y + 10$$

$$x - y = 12 + y$$

Solution

Question 7

$$3x - y + 14 = 24$$

$$2x - y = 0$$

$$3x + 2p = q + x$$

$$x^{3} + y^{3} = 13$$

Solution

Question 8

$$x + y = 5000$$

$$x - y = 5000$$

$$x + y+5000=0$$

None of these

Solution

Question 9

$$5+4x=y+3$$

$$x+2y=y-x$$

$$3-x={y}^{2}+4$$

$$x+y=0$$

Solution

Question 10

$$x + 2y = 0$$

$$x - 2y = 0$$

$$2x + y = 0$$

$$2x - y = 0$$

Solution

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