1 Marks Question

Question 11 Mark

Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y =k.

Answer

Given linear equation is
2x+3y=k
take x=2 & y=1 then,
2(2)+3(1)
=4+3
=7
so, k=7

Question 21 Mark

Find whether (1, 1) is the solution of the equation x – 2y = 4 or not.

Answer

Put x = 1 and y = 1 in given equation, we get
x – 2y = 1 – 2(1) = 1 – 2 = –1, which is not 4.
∴ (1, 1) is not a solution of given equation.

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Question 31 Mark

Find whether(4, 0) is the solution of the equation x – 2y = 4 or not?

Answer

x-2y=4

Put x = 4 and y = 0 in given equation, we get
x – 2y = 4 – 2(0) = 4
∴ (4, 0) is a solution of given equation.

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Question 41 Mark

Find whether (2, 0) is the solution of the equation x – 2y = 4 or not?

Answer

x-2y=4

Put x = 2 and y = 0 in given equation, we get

x – 2y = 2 – 2(0) = 2 – 0 = 2, which is not 4.
∴ (2, 0) is not a solution of given equation.

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Question 51 Mark

Which one of the options is true, and why? y = 3x + 5 has

Answer

infinitely many solutions

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Question 61 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in 5 = 2x.

Answer

We need to express the linear equation 5 = 2x in the form ax + by + c = 0 and indicate the values of a, b and c.
$5 = 2x{\text{ can also be written as }} - 2x + 0 \cdot y + 5 = 0.$
We need to compare the equation $ - 2x + 0 \cdot y + 5 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = - 2,b = 0{\text{ and }}c = 5$

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Question 71 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in y - 2 = 0.

Answer

We need to express the linear equation y - 2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c.
$y - 2 = 0{\text{ can also be written as }}0 \cdot x + 1 \cdot y - 2 = 0.$
We need to compare the equation $0 \cdot x + 1 \cdot y - 2 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = 0,b = 1{\text{ and }}c = - 2$

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Question 81 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in 3x + 2 = 0.

Answer

We need to express the linear equation 3x + 2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c.
$3x + 2 = 0{\text{ can also be written as }}3x + 0 \cdot y + 2 = 0.$
We need to compare the equation $3x + 0 \cdot y + 2 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = 3,b = 0{\text{ and }}c = 2$

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Question 91 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in 2x = -5y.

Answer

We need to express the linear equation $2x=-5y$ in the form ax + by + c = 0 and indicate the values of a, b and c.
$2x = - 5y{\text{ can also be written as }}2x + 5y + 0 = 0.$
We need to compare the equation $2x + 5y + 0 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = 2,b = 5{\text{ and }}c = 0$

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Question 101 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in x = 3y.

Answer

We need to express the linear equation $x = 3y$ in the form ax + by + c = 0 and indicate the values of a, b and c

$x = 3y{\text{ can also be written as }}x - 3y + 0 = 0.$
We need to compare the equation $x - 3y + 0 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = 1,b = - 3{\text{ and }}c = 0$

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Question 111 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in -2x + 3y = 6.

Answer

We need to express the linear equation $ - 2x + 3y = 6$ in the form ax + by + c = 0 and indicate the values of a, b and c.
$ - 2x + 3y = 6{\text{ can also be written as }} - 2x + 3y - 6 = 0.$
We need to compare the equation $ - 2x + 3y - 6 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $a = - 2,b = 3{\text{ and }}c = - 6$

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Question 121 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in $x - \frac{y}{5} - 10 = 0$

Answer

We need to express the linear equation $x - \frac{y}{5} - 10 = 0$ in the form ax + by + c = 0 and indicate the values of a, b and c.

$x - \frac{y}{5} - 10 = 0{\text{ can also be written as 1}} \cdot x - \frac{y}{5} - 10 = 0.$

We need to compare the equation ${\text{1}} \cdot x - \frac{y}{5} - 10 = 0$ with the general equation ax + by + c = 0, to get the values of a, b and c.

Therefore, we can conclude that $a = 1,b = - \frac{1}{5}{\text{ and }}c = - 10$

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Question 131 Mark

Express the linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in $2x + 3y = 9.3\overline 5$

Answer

$2x + 3y = 9.3\overline 5 $
We need to express the linear equation $ 2x + 3y = 9.3\overline 5 $ in the form ax + by + c = 0 and indicate the values of a, b and c.
$2x + 3y = 9.3\overline 5 {\text{ can also be written as }}2x + 3y - 9.3\overline 5 = 0.$
We need to compare the equation $2x + 3y - 9.3\overline 5 = 0$
with the general equation ax + by + c = 0, to get the values of a, b and c.
Therefore, we can conclude that $ a = 2,b = 3{\text{ and }}c = - 9.3\overline 5 $

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Question 141 Mark

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).

Answer

Let the cost of a notebook be ₹ x.
Let the cost of a pen be ₹ y.
We need to write a linear equation in two variables to represent the statement, “Cost of a notebook is twice the cost of a pen”.
Therefore, we can conclude that the required statement will be x = 2y.

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Question 151 Mark

Give the point (1, 2), find the equation of a line on which it lies. How many such equations are there?

Answer

Here (1, 2) is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point (1, 2). One example of such a linear equation is x + y = 3.
Others are y – x = 1, y = 2x, since they are also satisfied by the coordinates of the point (1, 2). In fact, there are infinitely many linear equations which are satisfied by the coordinates of the point (1, 2).

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Question 161 Mark

Find two solutions for equation: 3y + 4 = 0

Answer

Writing the equation 3y + 4 = 0 as 0.x + 3y + 4 = 0, you will find that y = $-\frac{4}{3}$ for any value of x.
Thus, two solutions can be given as $\left(0,-\frac{4}{3}\right) \text { and }\left(1,-\frac{4}{3}\right)$

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Question 171 Mark

Find two solutions for equation: 2x + 5y = 0

Answer

Taking x = 0, we get 5y = 0, i.e., y = 0. So (0, 0) is a solution of the given equation.
Now, if you take y = 0, you again get (0, 0) as a solution, which is the same as the earlier one.
To get another solution, take x = 1, say.
Then you can check that the corresponding value of y is $-\frac{2}{5} \cdot \operatorname{So}\left(1,-\frac{2}{5}\right)$ is another solution of 2x + 5y = 0

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Question 181 Mark

Find two solutions for equation 4x + 3y = 12

Answer

Taking x = 0, we get 3y = 12, i.e., y = 4.
So, (0, 4) is a solution of the given equation.
Similarly, by taking y = 0, we get x = 3.
Thus, (3, 0) is also a solution

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Question 191 Mark

Write an equation in two variables: 5y = 2

Answer

5y = 2 can be written as 0.x + 5y – 2 = 0

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Question 201 Mark

Write equation in two variables: 2x = 3

Answer

2x = 3 can be written as 2x + 0.y – 3 = 0

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Question 211 Mark

Write an equation in two variables: y = 2

Answer

y = 2 can be written as 0.x + 1.y = 2, or 0.x + 1.y – 2 = 0

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Question 221 Mark

Write an equation in two variables: x = –5

Answer

x = –5 can be written as 1.x + 0.y = –5, or 1.x + 0.y + 5 = 0

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Question 231 Mark

Write the equation in the form ax + by + c = 0 and indicate the values of a, b and c: 2x = y

Answer

The equation 2x = y can be written as 2x – y + 0 = 0. Here a = 2, b = –1 and c = 0

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Question 241 Mark

Write the equation in the form ax + by + c = 0 and indicate the values of a, b and c : 4 = 5x – 3y

Answer

The equation 4 = 5x – 3y can be written as 5x – 3y – 4 = 0. Here a = 5, b = –3 and c = – 4

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Question 251 Mark

Write the equations in the form ax + by + c = 0 and indicate the values of a, b and c: x – 4 = $\sqrt3$y

Answer

The equation x – 4 = $\sqrt3$y can be written as x – $\sqrt3$y – 4 = 0.
Here a = 1, b = – $\sqrt3$ and c = – 4

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Question 261 Mark

Write the equation in the form ax + by + c = 0 and indicate the values of a, b and c : 2x + 3y = 4.37

Answer

We have 2x + 3y = 4.37 can be written as 2x + 3y – 4.37 = 0. Here a = 2, b = 3 and c = – 4.37

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