Question

Solve the following pair of linear equations graphically. Also write the observations.

(iii) 3x - y = 2 ; 9x - 3y = 6​

Answer 1

Step-by-step explanation:

Given:

$\begin{gathered}\begin{gathered}3x-y=2 \\9x -3y = 6 \\ \end{gathered} \end{gathered}$

To find: Solution of linear pair of equation graphically.

Solution:

Step 1: Find points to plot 3x-y=2

Put x=0

0-y=2

y=-2

let it is point A(0,-2)

Put y=4

3x-4=2

3x=6

x=2

let it is point B(2,4)

Plot points on graph,make a straight line by joining these points.

Step 2: Find points to plot 9x-3y=6

Put x=-1

-9-3y=6

y= -5

let it is point C(-1,-5)

Put y=10

9x-30=6

x=4

let it is point D(4,10)

Plot points on graph,make a straight line by joining these points.

Graph is attatched.One line is dashed and one is plane,so that it will distinguish.

It is clearly shown that both the lines are coincide (Overlapping); they meet at infinite time.

Therefore,these linear equation has infinite many solution.

Final answer:

Given pair of linear equations have infinite many solution.

System of equations is consistent.

Hope it helps you.

To learn more on brainly:

solve the following system of linear equation graphically: 3x+y-11=0 and x-y-1=0

shade the region bounded by these lines...

https://brainly.in/question/3050092

Answer 2

Solve the following pair of linear equations graphically. Also write the observations.

↪️ 3x - y = 2 ; 9x - 3y = 6

Firstly let us consider,

• 3x - y = 2 as equation 1
• 9x - 3y = 6 as equation 2

Step by step explanation:

~ Firstly let us put x as 0 in equation 1

↪️ 3x - y = 2

↪️ 3(0) - y = 2

↪️ 0 - y = 2

↪️ -y = 2

↪️ y = -2

• Therefore, (0,-2) is coordinate

~ Now let us put y as 0 in equation 1

↪️ 3x - y = 2

↪️ 3x - 0 = 2

↪️ 3x = 2

↪️ x = 2/3

• Therefore, (2/3,0) is coordinate

~ Now let us put x as 0 in equation 2

↪️ 9x - 3y = 6

↪️ 9(0) - 3y = 6

↪️ 0 - 3y = 6

↪️ -3y = 6

↪️ y = 6/-3

↪️ y = -2

• Therefore, (0,-2) is coordinate

~ Now let us put x as 0 in equation 2

↪️ 9x - 3y = 6

↪️ 9x - 3(0) = 6

↪️ 9x - 0 = 6

↪️ 9x = 6

↪️ x = 6/9

↪️ x = 2/3

• Therefore, (2/3,0) is coordinate

What we observe?

↪️ We observe that the coordinate(s) in both equation as the same axis coming same. Therefore, according to the third attachment the lines are on each other.

Additional information:

The system used for describing the position of a point in the plane is known as cartesian system.

Relation between the signs of the coordinates of a point and the quadrant of a point in which it lie.

1) If the point is in the first quadrant then the point will be in the form of (+,+) since the 1st quadrant is enclosed by the positive x-axis and positive y-axis

2) If the point is in the second quadrant then the point will be in the form of (-,+) since the 2nd quadrant is enclosed by the negative x-axis and positive y-axis

3) If the point is in the third quadrant then the point will be in the form of (-,-) since the 3rd quadrant is enclosed by the negative x-axis and negative y-axis

4) If the point is in the fourth quadrant then the point will be in the form of (+,-) since the 4th quadrant is enclosed by the positive x-axis and negative y-axis

Kindly see this concept from attachment 4th.

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Note: As I take x and y as 0 in the equations, so it is not compulsory to take it like that, you can take any number for this but be same. But it is better to take 0 as x and y, vice versa but again choice is yours. Thanks for understanding!