3 Marks Question - MATHS STD 9 Questions - Vidyadip

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3 Marks Question

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19 questions · timed · auto-graded

Question 13 Marks

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
5x - 2y = 10

Answer

We are given, 5x - 2y = 10 Substituting x = 0 in the given equation, We get; 5 × 0 - 2y = 10 - 2y = 10 - y $=\frac{10}{2}$ y = -5 Thus x = 0 and y = -5 is the solution of 5x - 2y = 10 Substituting y = 0 in the given equation, we get 5x - 2 × 0 = 10 5x = 10$\text{x} = \frac{10}{5}$
x = 2 Thus x = 2 and y = 0 is a solution of 5x - 2y = 10

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Question 23 Marks

Give the geometric representations of the following equations:

On the number line.
On the Cartesain plane.

x = 2

Answer

x = 2
Point A represents x = 2 number line.
On Cartesian plane, eqution represents all points on y axis for which x = 2

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Question 33 Marks

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
2x + 3y = 24

Answer

We are given, 2x + 3y = 24
Substituting x = 0 in the given equation, we get; 2 × 0 + 3y = 24
3y = 24
$\text{y}=\frac{24}{3}$
y = 8
Thus x = 0 and y = 8 is a solution of 2x + 3y = 24
Substituting y = 0 in the given equation, we get;
2x + 3 × 0 = 24
2x = 24
$\text{x} = \frac{24}{2}$
x = 12
Thus x = 12 and y = 0 is a solution of 2x + 3y = 24

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Question 43 Marks

Give the geometric representations of the following equations:

On the number line.
On the Cartesain plane.

y = 3

Answer

y = 3
Point A represents 3 on number line.
On Cartesian plane, equation represents all points on x axis for which y = 3

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Question 53 Marks

If $x = 1$ and $y = 6$ is a solution of the equation $8x - ay + a^2 = 0,$ find the values of $a.$

Answer

We are given,
$8x - ay + a^2 = 0 (1, 6)$ is a solution of equation $8x - ay + a^2 = 0$
Substituting $x = 1$ and $y = 6$ in $8x - ay + a^2 = 0,$
we get $8 \times 1 - a \times 6 + a^2 = 0$
$\Rightarrow a^2 - 6a + 8 = 0$
Using quadratic factorization $a^2 - 4a - 2a + 8$
$= 0 a(a - 4) - 2(a - 4)$
$= 0 (a - 2)(a - 4) = 0$
$a = 2, 4$

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Question 63 Marks

Write two solutions for the following equations:
x = 6y

Answer

We are given,
x = 6y
Substituting x = 0 in the given equation, we get
0 = 6y
$\text{y}=\frac{0}{6}$
y = 0
Thus x = 0 and y = 0 is the solution of x = 6y
Substituting x = 6 in the given equation, we get
6 = 6y
$\text{y}=\frac{6}{6}$
y = 1
Thus x = 6 and y = 1 is the solution of x = 6y

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Question 73 Marks

If x = 2a + 1 and y = a -1 is a solution of the equation 2x - 3y + 5 = 0, find the value of a.

Answer

We are given,
2x - 3y + 5 = 0 (2a + 1, a - 1) is the solution of equation 2x - 3y + 5 = 0.
Substituting x = 2a + 1 and y = a - 1 in 2x - 3y + 5 = 0,
We get 2 × 2a + (1- 3) × a - 1 + 5 = 0
⇒ 4a + 2 - 3a + 3 + 5 = 0
⇒ a + 10 = 0
⇒ a = -10

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Question 83 Marks

Give the geometric representations of the following equations:

On the number line.
On the Cartesain plane.

3x - 5 = 0

Answer

3x - 5 = 0
3x = 5
$\text{x}=\frac{5}{3}=1\frac{2}{3}=1.6\text{ (Approx)}$
Point A represents $1\frac{1}{2}$ or $\frac{5}{3}$ on number line.
On Cartesian plane, equation represents all points on y axis for which x = 1.6

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Question 93 Marks

Give the geometric representations of the following equations:

On the number line.
On the Cartesain plane.

2x + 9 = 0

Answer

2x + 9 = 0
2x = -9
$\text{X}=\text{x}=\frac{-9}{2}=-4.5$
Point A represents -4.5 on the number line.
On Cartesian plane, equation represents all points on y axis for which x = -4.5

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Question 103 Marks

Give the geometric representations of the following equations:

On the number line.
On the Cartesain plane.

y + 3 = 0

Answer

y + 3 = 0
y = -3
Point A represents -3 on number line.
On Cartesian plane, equation represents all points on x axis for which y = -3

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Question 113 Marks

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
-4x + 3y = 12

Answer

We are given, -4x + 3y = 12
Substituting x = 0 in the given equation, we get;
-4 × 0 + 3y = 12
3y = 12
y = 4
Thus x = 0 and y = 4 is a solution of the -4x + 3y = 12
Substituting y = 0 in the given equation, we get;
-4x + 3 × 0 = 12 - 4x = 12
$\text{x} = -\frac{12}{4}$
x = -3
Thus x = -3 and y = 0 is a solution of -4x + 3y = 12

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Question 123 Marks

Write two solutions for the following equations:
$\text{x}+\pi\text{y} = 4 $

Answer

We are given, $\text{x}+\pi\text{y} = 4 $ Substituting x = 0 in the given equation, we get $\text{x}+\pi\text{y} = 4 $ $\pi\text{y}=4-0$ $\text{y}=\frac{4}{\pi}$Thus x = 0 and $\text{y}=\frac{4}{\pi}$ is the solution of $\text{x}+\pi\text{y} = 4 $
Substituting x = 6 in the given equation, we get $\text{x}+\pi\text{y} = 4 $ $\pi\text{y}=4-0$ $\text{y}=\frac{0}{\pi}$ $\text{y}=0$ Thus x = 4 and y = 0 is the solution of $\text{x}+\pi\text{y} = 4 $

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Question 133 Marks

Solve the equation 2y - 1 = y + 1 and represent it graphically on the coordinate plane.

Answer

We are given,
2y - 1 = y + 1
we get,
2y - y = 1 + 1
y = 2
The representation of the solution on the Cartesian plane, it is a line parallel to y axis passing through the point (0, 2) is shown below

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Question 143 Marks

If the point (a, 2) lies on the graph of the linear equatio 2x - 3y + 8 = 0, find the value of a.

Answer

We are given (a, 2) lies on the graph of linear equation 2x - 3y + 8 = 0.
So, the given co-ordinates are the solution of the equation 2x - 3y + 8 = 0.
Therefore, we can calculate the value of a by substituting the value of given co-ordinates in equation 2x - 3y + 8 = 0.
Substituting x = a and y = 2 in equation 2x - 3y + 8 = 0, we get
2 × a - 3 × 2 + 8 = 0
2a - 6 + 8 = 0
2a + 2 = 0
2a = -2
$\text{a}=-\frac{2}{2}$
a = -1

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Question 153 Marks

Write two solutions for the following equations:
$\frac{2}{3}\text{x} - \text{y} = 4$

Answer

We are given,$\frac{2}{3}\text{x} - \text{y} = 4$
Substituting x = 0 in the given equation, we get
$\frac{2}{3}\text{x} - \text{y} = 4$
0 - y = 4
y = -4
Thus x = 0 and y = -4 is the solution of $\frac{2}{3}\text{x} - \text{y} = 4$
Substituting x = 6 in the given equation, we get
$\frac{2}{3}\text{x} - \text{y} = 4$
-y = 4 - 2
y = -2
Thus x = 3 and y = -2 is the solution of $\frac{2}{3}\text{x} - \text{y} = 4$

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Question 163 Marks

Give the geometrical representation of 2x + 13 = 0 as an equation in:
Two variables.

Answer

Two variable representation of 2x + 13 = 0
2x + 0y + 13 = 0
2x = 13 = 0
2x = -13
$\text{x}=-\frac{13}{2}=-6\frac{1}{2}$
On Cartesian plane, equation represents all points on y axis for which x = -6.5

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Question 173 Marks

Find the value of k for which the point (1, -2) lies on the graph of the linear equation
x - 2y + k = 0.

Answer

We are given (1, -2) lies on the graph of linear equation x - 2y + k = 0.
So, the given co-ordinates are the solution of the equation x - 2y + k = 0.
Therefore, we can calculate the value of k by substituting the value of given co-ordinates in equation x - 2y + k = 0.
Substituting x = 1 and y = -2 in equation 2x - 3y + 8 = 0, we get
1 - 2(-2) + k = 0
1 + 4 + k = 0
k = -5

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Question 183 Marks

Give the geometrical representation of 2x + 13 = 0 as an equation in:
One variable.

Answer

One variable representation of 2x + 13 = 0
2x = -13
$\text{x}=\frac{-13}{2}=-6\frac{1}{2}$
Point A represents $-\frac{13}{2}.$

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Question 193 Marks

Write two solutions for the following equations:
3x - 4y = 7

Answer

We are given,
3x 1 + 4y = 7
Substituting x = 1 in the given equation, we get
3x 1 + 4y = 7
4y = 7 - 3
$\text{y}=\frac{4}{4}$
Thus x = 1 and y = 1 is the solution of 3x + 4y = 7
Substituting x = 2 in the given equation, we get
3 × 2 + 4y = 7
$\text{y}=\frac{1}{4}$
$\text{y}=\frac{1}{4}$
Thus x = 2 and $\text{y}=\frac{1}{4}$ is the solution of 3x + 4y = 7

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