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CBSE Questions for Class 9 Maths Linear Equations In Two Variable Quiz 4 - MCQExams.com
CBSE
Class 9 Maths
Linear Equations In Two Variable
Quiz 4
Find the equation for the graph above.
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$$x = 3$$
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$$y = 3$$
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$$y = -5$$
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$$x = -5$$
Explanation
The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(3, -5)$$ is $$y = -5$$.
Find the equation for the graph above.
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$$x = -2$$
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$$y = -1$$
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$$y = -2$$
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$$x = -1$$
Explanation
The graph represents a line that is parallel to the $$x$$-axis and passes through the point $$(-2, -1)$$ is $$y = -1$$.
Which of the following equations is linear?
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$$y = \dfrac {3}{x}$$
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$$\sqrt {x} + y = 0$$
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$$\dfrac {1}{2}x - \dfrac {5}{8}y = 11$$
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$$y = x^{2} + 2x - 4$$
Explanation
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.
Which of the following is a linear equation in one variable?
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$$2x+1=y-3$$
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$$2t-1=3t+5$$
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$$2x-1=x^{2}$$
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$$x^{2}-x+1=0$$
Explanation
$$\textbf{Step - 1: Checking all options}$$
$$A) 2x+1=y-3$$
$$\text{We can see that the given equation has two variables x and y in and }$$
$$\text{hence is not a linear equation in}$$ $$\text{one variable}$$
$$B) 2t-1=3t+5$$
$$\text{We can clearly see that the given equation has only one variable t and}$$
$$\text{hence is a linear equation in one }$$$$\text{variable.}$$
$$C) 2x-1=x^2$$
$$\text{We can see that the given equation is not linear as its variable has}$$
$$\text{a power greater than one}$$
$$D) x^2-x+1=0$$
$$\text{We can see that the given equation is not linear as its variable has}$$
$$\text{a power greater than one}$$
$$\textbf{Thus, the equation }\mathbf{ 2t-1=3t+5}\textbf{ is a linear equation in one variable.}$$
Graph of the given linear equation is:
$$2y=-x+1$$
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Which of the following equations have graphs parallel to the $$x-$$axis?
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$$x+6=0$$
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$$y-3=0$$
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$$x+8=0$$
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$$y+4=0$$
The distance between the graphs of the equations $$y = -1$$ and $$y = 3$$ is
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$$2$$
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$$4$$
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$$3$$
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$$1$$
$$\textbf{State whether the statement is True or False.}$$
If $$9$$ is the solution of variable $$x$$ in the equation $$\dfrac{5x-7}{2}=y$$, then the value of $$y$$ is $$28$$.
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True
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False
Explanation
Given that, $$x=9$$ is solution of $$x$$ in $$y=\dfrac{5 x-7}{2}$$
Now, put the value of $$x$$ in of the equation. we get,
$$\begin{aligned}&\quad \frac{5(9)-7}{2}=y \\&\Rightarrow \quad \frac{45-7}{2}=y \\&\Rightarrow \quad \frac{38}{2}=y \\&\Rightarrow \quad y=19\end{aligned}$$
$$\textbf{Hence the given Statement is False.}$$
the pair of equations $$ x=a $$ and $$ y =b $$ graphically represents line which are
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Parallel
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intersecting at $$ (b , a) $$
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coincident
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intersecting at $$ (a , b ) $$
Explanation
$$ x= a $$ is the equation of straight line parallel to the y -axis at distance 'a ' from it again $$ y= b $$ is the equation of a straight line parallel to the x-axis at a distance 'b' from it.
so the pair of equations $$ x= a $$ and $$ y = b $$ graphically represents lines which are intersecting at $$ (a,b) $$
hence (d) is the correct answer.
The coordinates of points in the table:
Represent the solutions of the equation $$x - y + 2 = 0$$
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True
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False
Explanation
The points $$(0,2), (1,3), (2,4)$$ and $$(4,6)$$ satisfy the given equation $$x - y + 2 = 0.$$
Each of these points is the solution of the equation $$x - y + 2- 0.$$
But, in the equation if we put $$(3,-5)$$ i.e $$3-(-5) + 2 = 0,$$ i.e., $$3 + 5 = 0$$ or $$10 \neq 0,$$ it does not satisfy the equation, So, it is false.
hence, the given statement false, since the point $$(3,-5)$$ does not satisfy the given equation
Linear equation in one variable has
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Only one variable with any power.
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Only one term with a variable.
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Only one variable with power $$1$$.
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Only constant term.
Explanation
$$\textbf{Step - 1: Defining}$$
$$\text{A linear equation is a relation between variables of degree 1. }$$
$$\text{A linear equation in one variable is a relation of a variable of power 1}$$
$$\textbf{Hence a linear equation in one variable has only one variable with power 1}$$
State weather the statement is true(T) or false (F):
Two different equations can never have the same answer.
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True
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False
Explanation
False,
Two different equations may have the same answer.
eg. $$2x+1=2$$ and $$2x-5=-4$$ are the two linear equations whose solutions are $$\cfrac12$$.
To draw graph of $$4x + 5y = 19$$, Find y when x = 1
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4
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3
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2
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-3
Explanation
$$4x + 5y = 19$$
When x = 1, then y will be
$$4(1) + 5y = 19$$
$$\Rightarrow 4 + 5y = 19$$
$$\Rightarrow 5y = 19 - 4 = 15$$
$$\Rightarrow 5y = 15$$
$$\Rightarrow y = \dfrac{15}{5} = 3$$
Hence, the correct answer is 3.
The name of the graph of $$y = 2x + 3$$ is called
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Parabola
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Hyper bola
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Straight line
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Bar graph
Which of the following could be a graph of the function $$y = 1 /x$$?
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Read the following statements carefully and select the correct option.
Statement-I : The graph of the linear equation $$x + 2y = 6$$ passes through $$(8, -1)$$.
Statement II : Every point which satisfies the linear equation is a solution of the equation.
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Both Statement-I and Statement-II are true.
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Only Statement-I is true.
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Only Statement-II is true.
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Neither Statement-I nor Statement-II are true.
Explanation
Consider statement I:
Put the given point in equation,
$$8+2(-1)=8-2=`6=RHS$$
Hence given point satisfies the equation of line.
Hence statement I is true
Consider statement II:
Every point lying on the line satisfies the equation of line
As we see from statement I that the point that satisfies the equation of the line is a solution.
Hence statement II is true
If point ( 4,2 ) lies on the graph of the equation 5x + aY =28 then a=?
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8
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4
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20
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2
Graphical solution of x+y=2 is
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The equation of $$x$$-axis is ____.
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$$x=0$$
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$$y=0$$
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$$x=a$$
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$$y=a$$
Draw the graph of each of the following liner equations in two variables
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x + y = 4
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x - y = 2
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y = 3x
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3 = 2x +y
If m and b are real nubers and mb>0, then the line whose equation y =mx+b cannot contain point.
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(0, 2009)
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(2009, 0)
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(0, -2009)
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(20, -100)
The graph $$y=3$$ is __________________.
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the $$x$$-axis
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the $$y$$-axis
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a line parallel to the $$x$$- axis
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a line parallel to the $$y$$- axis
Which of the equation given below have graphs parallel to the X-axis and which ones have graphs parallel to the Y-axis?
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$$x = 3$$
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$$y - 2 = 0$$
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$$x + 6 = 0$$
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$$y = - 5$$
The graph is shown, then the number of solutions of f(f(x))=2 will be
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1
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2
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3
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4
The number of values of z which satisfies both the equation $$\left|x-1-i \right|=\sqrt{2}$$ and $$\left|x-1-i \right|={2}$$, is
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1
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0
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2
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infinitely many
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Incorrect : 0
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