show graphically that the system of equations 3x-6y+9=0; 2x-4y+6=0 has infinitely many solutions. I will mark you as brainliest please answer
Answers
EXPLANATION.
Show graphically that the system of equation has infinitely many solutions.
⇒ 3x - 6y + 9 = 0. - - - - - (1).
⇒ 2x - 4y + 6 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 3x - 6y + 9 = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 3(0) - 6y + 9 = 0.
⇒ - 6y + 9 = 0.
⇒ 6y = 9.
⇒ y = 9/6.
⇒ y = 1.5.
Their Co-ordinates = (0,1.5).
Put the value of y = 0 in the equation, we get.
⇒ 3x - 6(0) + 9 = 0.
⇒ 3x + 9 = 0.
⇒ 3x = - 9.
⇒ x = - 3.
Their Co-ordinates = (-3,0).
From equation (2), we get.
2x - 4y + 6 = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) - 4y + 6 = 0.
⇒ - 4y + 6 = 0.
⇒ 4y = 6.
⇒ y = 1.5.
Their Co-ordinates = (0,1.5).
Put the value of y = 0 in the equation, we get.
⇒ 2x - 4(0) + 6 = 0.
⇒ 2x + 6 = 0.
⇒ 2x = - 6.
⇒ x = - 3.
Their Co-ordinates = (-3,0).
As we can see that both curves overlap each other.it means it is infinitely many solutions.
Given :-
3x - 6y + 9 = 0
2x - 4y + 6 = 0
To Find :-
Prove that it infinitely many solutions
Solution :-
3x - 6y + 9 = 0
3x - 6y = 0 - 9
3x - 6y = -9
Putting x as 0
3(0) - 6y = -9
0 - 6y = -9
- 6y = -9
y = -9/-6
y = 9/6
y = 3/2
Coordinates = (0,3/2)
Putting y as 0
3x - 6(0) = -9
3x - 0 = -9
3x = -9
x = -9/3
x = -3
Coordinate = (-3,0)
In Eq 2
2x - 4y + 6 = 0
2x - 4y = 0- 6
2x - 4y = -6
Putting x as 0
2(0) - 4y = - 6
0 - 4y = - 6
- 4y = - 6
y = - 6/- 4
y = 6/4
y = 3/2
Coordinate = (0,3/2)
Putting y as 0
2x - 4(0) = - 6
2x - 0 = -6
2x = -6
x = -6/2
x = -3
Coordinate = (-3,0)