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

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 161 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 171 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 181 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 191 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 201 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 211 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 221 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 231 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 241 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 251 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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