Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Which equation represents the line that passes through the point $$(-1, 4)$$ and is parallel to the $$y$$-axis?

A
$$y = -1$$

B
$$x = -1$$

C
$$x = 4$$

D
$$y = 4$$

Solution

The graph represents a line that is parallel to the $$y$$-axis and passes through the point $$(-1, 4)$$ is $$x = -1$$.
Question 2
1 / -0

What is the equation for the graph shown above?

A
$$y = 2$$

B
$$y = -4$$

C
$$x = 2$$

D
$$x = -4$$

Solution

We can observe from the given graph that the line is parallel to the $$y$$-axis and passes through the point $$(-4, 2)$$.
Hence, it represents $$x = -4$$.
Question 3
1 / -0

Which equation represents the line that passes through the point $$(-5, -4)$$ and is parallel to the $$y$$-axis?

A
$$x = -5$$

B
$$x = -4$$

C
$$y = -5$$

D
$$y = -4$$

Solution

Equation of line parallel to $$y-$$axis is of the form $$x=a$$
$$x-$$co-ordinate of this line remains same throughout. Also it is given that it passes through $$(-5,-4)$$.
Thus required equation of line is $$x=-5$$
Question 4
1 / -0

Identify the equation for the above graph.

A
$$x = 2$$

B
$$x = 4$$

C
$$y = 4$$

D
$$y = 2$$

Solution

The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(2, 4)$$.
Since it is parallel to x-axis and passes through $$(2,4)$$ therefore its equation is $$y = 4$$.
Question 5
1 / -0

Find the equation for the graph above.

A
$$x = -2$$

B
$$y = -1$$

C
$$y = -2$$

D
$$x = -1$$

Solution

The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(-2, -1)$$ is $$y = -1$$.
Question 6
1 / -0

Find the equation for the graph above.

A
$$x = 3$$

B
$$y = 3$$

C
$$y = -5$$

D
$$x = -5$$

Solution

The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(3, -5)$$ is $$y = -5$$.
Question 7
1 / -0

Which of the following equations is linear?

A
$$y = \dfrac {3}{x}$$

B
$$\sqrt {x} + y = 0$$

C
$$\dfrac {1}{2}x - \dfrac {5}{8}y = 11$$

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

Solution

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable (however, different variables may occur in different terms)
Degree of linear equation is $$1$$
In first option, highest power of $$y$$ is $$1$$ but highest power of $$x$$ is $$-1$$
In second option, highest power of $$y$$ is $$1$$ but highest power of $$x$$ is $$\dfrac{1}{2}$$
In third option, highest power of $$x$$ is $$1$$ and highest power of $$y$$ is $$1$$
In fourth option, highest power of $$y$$ is $$1$$ but highest power of $$x$$ is $$2$$
Hence, option C is correct.
Question 8
1 / -0

Which of the following is not a linear equation?

A
$$x+y=6$$

B
$$x^2-5x+6=0$$

C
$$y=2x$$

D
$$x=0$$

Solution

$${x^2} - 5x + 6 = 0$$
It is a quadratic equation since the highest degree is 2.
It is not linear equation.
Question 9
1 / -0

Which of the following is a linear equation in one variable?

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

B
$$2t-1=3t+5$$

C
$$2x-1=x^{2}$$

D
$$x^{2}-x+1=0$$

Solution

$$\textbf{Step - 1: Checking all options}$$
$$A) 2x+1=y-3$$
$$\text{We can see that the given equation has two variables x and y in and }$$
$$\text{hence is not a linear equation in}$$ $$\text{one variable}$$

$$B) 2t-1=3t+5$$
$$\text{We can clearly see that the given equation has only one variable t and}$$
$$\text{hence is a linear equation in one }$$$$\text{variable.}$$

$$C) 2x-1=x^2$$
$$\text{We can see that the given equation is not linear as its variable has}$$
$$\text{a power greater than one}$$

$$D) x^2-x+1=0$$
$$\text{We can see that the given equation is not linear as its variable has}$$
$$\text{a power greater than one}$$
$$\textbf{Thus, the equation }\mathbf{ 2t-1=3t+5}\textbf{ is a linear equation in one variable.}$$
Question 10
1 / -0

Graph of the given linear equation is:
$$2y=-x+1$$

A

B

C

D

Solution