Test: Linear Equations In Two Variables - 2 - Class 9 MCQ

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.

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

There are infinitely many lines that can pass through a single point. Here’s why

• A point in geometry has no dimensions; it is simply a location.
• A line is defined by two points.
• Given one point, you can choose any other point in the plane, and a line can be drawn through these two points.
• Since there are infinitely many points that can be chosen as the second point, there are infinitely many lines that can pass through the initial point.

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.

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.

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

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

=> 3k + 3 = 6

=> 3k = 3

Hence, k = 1

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

The correct answer is C: 2x – 5y = 0.

- A linear equation in two variables can be written in the form ( ax + by = c ), where ( a ), ( b ), and ( c ) are constants.
- Option C: ( 2x - 5y = 0 ) fits the form ( ax + by = c ), making it linear.