2 Marks Questions

Question 12 Marks

Write the equation of a line parallel to y-axis and passing through the point (-3, -7).

Answer

We are given the co-ordinates of the Cartesian plane at (-3, -7).
For the equation of the line parallel to y axis, we assume the equation as a one variable equation independent of y containing x equal to -3.
We get the equation as x = -3

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Question 22 Marks

Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

Answer

We are given the co-ordinates of the Cartesian plane at (3, 5).
For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to 5.
We get the equation as y = 5

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Question 32 Marks

Find the value of $\lambda$ if $\text{x}=-\lambda$ and $\text{y} = \frac{5}{2}$ is a solution of the equation x + 4y - 7 = 0

Answer

We are given, x + 4y - 7 = 0 $(-\lambda, -5)$ is a solution of equation 3x + 4y = k
Substituting $\text{x}=-\lambda$ and $\text{y} = \frac{5}{2}$ in x + 4y - 7 = 0,
We get; $-\lambda+ 4 \times\Big(\frac{5}{2}\Big) - 7 $
$= 0 -\lambda + 4 \times\frac{5}{2} - 7 = 0$
$\lambda = 10 - 7$
$\lambda = 3$

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Question 42 Marks

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. lf units and ten's digit of the number are x ard y respectively, then write the linear equation representing the above statement.

Answer

Total original number is 10y + x.
The new number is obtained after reversing the order of digits is 10x + y.
According to question,
(10y + x) + (10x + y) = 121
⇒ 10y + x 10x + y = 121
⇒ 11x + 11y = 121
⇒ x + y = 11
This is the required linear equation for the given information.

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Question 52 Marks

A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

Answer

Total original number is 10y + x.
The new number is obtained after reversing the order of digits is 10x + y.
According to question,
10y + x = 10x + y + 27
⇒ 9y - 9x = 27
⇒ y - x = 3
⇒ x - y + 3 = 0
This is the required linear equation for the given information.

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Question 62 Marks

Check the following are solutions of the equation 2x - y = 6 and which are not:
(2, -2)

Answer

We are given, 2x - y = 6In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6 Substituting x = 2 and y = -2 in 2x - y, We get L.H.S = 2 × 2 - (-2) = 6 ⇒ L.H.S = R.H.S ⇒ (2, -2) is a solution of 2x - y = 6.

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Question 72 Marks

Check the following are solutions of the equation 2x - y = 6 and which are not:
(0, 6)

Answer

We are given, 2x - y = 6
In the equation 2x - y = 6,
We have L.H.S= 2x - y and R.H.S = 6
Substituting x = 0 and y = 6 in 2x - y
We get L.H.S = 2 × 0 - 6 = - 6
⇒ L.H.S ≠ R.H.S
⇒ (0, 6) is not a solution of 2x - y = 6.

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Question 82 Marks

If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of k.

Answer

It is given that (2, -2) is a solution of the equation 5x + ky = 4
$\therefore$ 5 × 2 + k × (-2) = 4
⇒ 10 - 2k = 4
⇒ -2k = 4 - 10
⇒ -2k = -6
$\Rightarrow\text{k}=\frac{6}{2}$
⇒ k = 3

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Question 92 Marks

Check the following are solutions of the equation 2x - y = 6 and which are not:
(3, 0)

Answer

We are given, 2x - y = 6
In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting x = 3 and y = 0 in 2x - y,
We get L.H.S = 2 × 3 - 0 = 6
⇒ L.H.S = R.H.S
⇒ (3, 0) is a solution of 2x - y = 6.

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Question 102 Marks

Check the following are solutions of the equation 2x - y = 6 and which are not:
$\Big(\frac{1}{2},\ -5\Big)$

Answer

We are given, 2x - y = 6
In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting $\text{x} = \frac{1}{2}$ and y = in 2x - y, we get L.H.S $=2\times\Big(\frac{1}{2}\Big) - (-5)$
⇒ 1 + 5 = 6
⇒ L.H.S = R.H.S
⇒ (12, -5) is a solution of 2x - y = 6.

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Question 112 Marks

Check the following are solutions of the equation 2x - y = 6 and which are not:
$(\sqrt{3}, 0)$

Answer

We are given, 2x - y = 6
In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting $\text{x} = \sqrt3$ and y = 0 in 2x - y,
We get L. H. S $= 2 \times \sqrt3 - 0$
⇒ L.H.S ≠ R.H.S
⇒ $(\sqrt{3}, 0)$ is not a solution of 2x - y = 6.

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Question 122 Marks

The cost of ball pen is Rs. 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Answer

Let the cost of fountain pen be y and cost of ball pen be x.
According to the given equation, we have
$\text{x}=\frac{\text{y}}{2}-5$
⇒ 2x = y - 10
⇒ 2x - y + 10 = 0
Here y is the cost of one fountain pen and x is that of one ball pen.

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Question 132 Marks

Solve the equation 3x + 2 = x - 8, and represent the solution on:
The Cartesian plane.

Answer

On Cartesian plane, equation represents all points on y axis for which x = -5

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Question 142 Marks

Plot the points (3, 5) and (-1, 3) on a graph paper an verify that the straight line passing through these points also passes through the point (1, 4).

Answer

The given points on the graph:

It is dear from the graph, the straight line passing through these points also passes through the point (1, 4).

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Question 152 Marks

If x = -1, y = 2 is a solution of the equation 3x + 4y = k, find the value of k.

Answer

We are given, 3x + 4y = k
Given that, (-1, 2) is the solution of equation 3x + 4y = k.
Substituting x = -1 and y = 2 in 3x + 4y = k,
We get; 3x - 1 + 4 × 2 = k
K = -3 + 8
k = 5

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Question 162 Marks

Solve the equation 3x - 2 = 2x + 3 and represent the solulion on the number line.

Answer

We are given,
3x - 2 = 2x + 3
we get,
3x - 2x = 3 + 2
x = 5
The representation of the solution on the number line, when given equation is treated as an equation in one variable.

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Question 172 Marks

Write the equation of a line Passing through the point (0, 4) and parallel to x-axis.

Answer

We are given the co-ordinates of the Cartesian plane at (0, 4).
For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to 4.
We get the equation as y = 4

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Question 182 Marks

A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.

Answer

We are given the co-ordinates of the Cartesian plane at (-4, 6).
For the equation of the line parallel to x axis, we assume the equation as a one variable equation independent of x containing y equal to 6.
We get the equation as y = 6

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Question 192 Marks

Solve the equation 3x + 2 = x - 8, and represent the solution on:
The number line.

Answer

3x + 2 = x - 8
⇒ 3x - x = -8 - 2
⇒ 2x = -10
⇒ x = -5
Points A represents -5 on number line.

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