Question

Solve graphically 3x - 2y = 6 and 3x + y = 15 Find the coordinates of the vertices of the triangle formed by these lines and x-axis.​

Answer 1

EXPLANATION.

Graphically.

⇒ 3x - 2y = 6. - - - - - (1).

⇒ 3x + y = 15. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 3x - 2y = 6. - - - - - (1).

Put the value of x = 0 in the equation, we get.

⇒ 3(0) - 2y = 6.

⇒ - 2y = 6.

⇒ y = - 3.

Their Co-ordinates = (0,-3).

Put the value of y = 0 in the equation, we get.

⇒ 3x - 2(0) = 6.

⇒ 3x = 6.

⇒ x = 2.

Their Co-ordinates = (2,0).

From equation (2), we get.

⇒ 3x + y = 15. - - - - - (2).

Put the value of x = 0 in the equation, we get.

⇒ 3(0) + y = 15.

⇒ y = 15.

Their Co-ordinates = (0,15).

Put the value of y = 0 in the equation, we get.

⇒ 3x + (0) = 15.

⇒ 3x = 15.

⇒ x = 5.

Their Co-ordinates = (5,0).

The Co-ordinates of the vertices of the triangle formed by these lines and x-axes = (4,3).

Answer 2

Given :-

3x - 2y = 6

3x + y = 15

To Find :-

Coordinates of the vertices of the triangle formed by these lines and x-axis.​

Solution :-

Put the value of x as 0

3(0) - 2y = 6

0 - 2y = 6

-2y = 6

y = -6/2

y = -3

Coordinates = (0,-3)

Put the value of y as 0

3x - 2(0) = 6

3x - 0 = 6

3x = 6

x = 6/3

x = 2

Coordinate = (2,0)

In Eq 2

Put the value of x as 0

3(0) + y = 15

0 + y = 15

y = 15

Coordinate = (0,15)

Put the value of y as 0

3x + 0 = 15

3x = 15

x = 15/3

x = 5

Coordinate = (5,0)

Vertices = (4,3)