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QUESTION: 1

x = 0 is the equation of

Solution:
Vertical lines cannot be written in standard form because the slope is undefined. The equation of the line is given by the x-intercept of the line. In this case x=0 goes though the origin (x=0), which means this is the equation of the y-axis.

QUESTION: 2

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.

Solution:

Given :

1. Five years ago a was three times as old as b

2. Ten years later a shall be twice older than b.

Assume that present age of a as x and that of b as y.

Five years ago, a was thrice as old as b

i.e. age of a was x - 5 and age of b was 3(y-5)

x - 5 = 3 (y - 5)

x - 5 = 3y - 15

x - 3y = -15+5

x - 3y = -10 ---------(1)

Ten years later, a shall be twice as old as b

i.e. age of a will be x + 10 and age of b will be 2(y+10)

x + 10 = 2 (y + 10)

x + 10 = 2y + 20

x - 2y = 20-10

x - 2y = 10 ---------(2)

By elimination method, we get

x - 3y = -10

x - 2y = 10

- y = -20

**y = 20 i.e. present age of b**

Substituting y = 20 in equation 1, we get

x - 3y = -10

x - 3(20) = -10

x - 60 = -10

x = -10 + 60

**x = 50 i.e. present age of a.**

QUESTION: 3

How many lines pass through two points?

Solution:

Only one straight line can pass through two points because the line will connect the two points as one as the initial and another point as the ending point.

QUESTION: 4

The graph of y = 4x will

Solution:

QUESTION: 5

For the equation 5x – 7y = 35, if y = 5, then the value of ‘x’ is

Solution:

QUESTION: 6

y = 0 is the equation of

Solution:

QUESTION: 7

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the total number of customers.

Solution:

**Step-by-step explanation:**

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines.

Let say There are C customers in a Line and total L number of lines

Total number of customers = ( customers in a line) * (number of Lines)

=>Total number of customers = CL

If one customer is extra in a line, then there would be two less lines

=> Total number of customers = (C + 1)(L -2)

(C + 1)(L -2) = CL

=> CL + L - 2C - 2 = CL

=> **L - 2C = 2 ** - eq 1

If one customer is less in line, there would be three more lines.

=> Total number of customers = (C - 1)(L +3)

(C - 1)(L +3) = CL

=> CL - L + 3C - 3 = CL

=> **- L + 3C = 3 ** - eq 2

Adding eq 1 & eq 2

=> **C = 5**

L - 2(5) = 2

=**> L = 12**

**5 **customers in a Line

Total Number of customers = CL = 5*12 = **60**

QUESTION: 8

How many lines pass through one point?

Solution:

QUESTION: 9

For what value of ‘k’, x = 2 and y = -1 is a solution of x + 3y – k = 0?

Solution:

QUESTION: 10

The area of the triangle formed by the line 2x + 5y = 10 and the coordinate axes is

Solution:

QUESTION: 11

The graph of the linear equation x + y = 0 passes through the point

Solution:

The graph of the linear equation x + y = 0 passes through the point (1,-1) because the co-ordinate of x and y axis satisfy the given equation

x + y = 0

1 - 1 = 0

so we can say (1,-1) is a solution of above equation

QUESTION: 12

The graph of the linear equation x + y = 0 passes through the point

Solution:

QUESTION: 13

The equation of a line parallel to x-axis and 3 units above the origin is

Solution:

QUESTION: 14

Which of the following pair is a solution of the equation 3x – 2y = 7?

Solution:

QUESTION: 15

Express ‘y’ in terms of ‘x’ in the equation 5x – 2y = 7.

Solution:

QUESTION: 16

A fraction becomes 1/3 when 1 is subtracted from its numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction

Solution:

QUESTION: 17

If (k, -3) lies on the line 3x – y = 6, then the value of ‘k’ is

Solution:

Putting x= k and y= -3 in the given equation,

i.e. 3(k) - (-3) = 6

=> 3k + 3 = 6

=> 3k = 3

Hence, k = 1

QUESTION: 18

The equation of a line parallel to x-axis and 5 units below the origin is

Solution:

QUESTION: 19

Which of the following is a linear equation in two variables?

Solution:

QUESTION: 20

Express ‘x’ in terms of ‘y’ in the equation 2x – 3y – 5 = 0.

Solution:

QUESTION: 21

The point of the form (a, a), where a ¹ 0 lies on

Solution:

QUESTION: 22

If x = 3 and y = -2 satisfies 2x – 3y = k, then the value of ‘k’ is

Solution:

QUESTION: 23

The equation of a line parallel to the y-axis and 4 units above the origin is

Solution:

QUESTION: 24

x = 5 and y = -2 is the solution of the linear equation

Solution:

QUESTION: 25

x – 4 is the equation of

Solution:

we know that the line parallel to y axis is given by x = a

x-4 = 0

x = 4

so it is a line parallel to y axis, at a distance of 4 units from it, to the right.

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