Question

Draw the graphs of x – y + 1 = 0 and 3x + 2y - 12 = 0. Determine the
coordinates of the vertices of the triangle formed by these lines and x axis
and shade the triangle.

Answer 1

EXPLANATION.

Graph of the equation.

⇒ x - y + 1 = 0. - - - - - (1).

⇒ 3x + 2y - 12 = 0. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ x - y + 1 = 0. - - - - - (1).

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

⇒ (0) - y + 1 = 0.

⇒ - y + 1 = 0.

⇒ - y = - 1.

⇒ y = 1.

Their Co-ordinates = (0,1).

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

⇒ x - (0) + 1 = 0.

⇒ x + 1 = 0.

⇒ x = - 1.

Their Co-ordinates = (-1,0).

From equation (2), we get.

⇒ 3x + 2y - 12 = 0. - - - - - (2).

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

⇒ 3(0) + 2y - 12 = 0.

⇒ 2y - 12 = 0.

⇒ 2y = 12.

⇒ y = 6.

Their Co-ordinates = (0,6).

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

⇒ 3x + 2(0) - 12 = 0.

⇒ 3x - 12 = 0.

⇒ 3x = 12.

⇒ x = 4.

Their Co-ordinates = (4,0).

Both curves intersects at a point = (2,3).

Answer 2

Given :-

x - y + 1 = 0

3x + 2y - 12 = 0

To Find :-

Determine the coordinates of the vertices of the triangle formed by these lines and x-axis  and shade the triangle.

Solution :-

x - y + 1 = 0

x - y = 0 - 1

x - y = -1

Put the value of x as 0

0 - y = -1

-y = -1

y = 1

If x = 0. Then, coordinate = (0,1)

Put the value of y as 0

x - 0 = -1

x = -1

If y = 0. Then, coordinate = (-1,0)

3x + 2y - 12 = 0

3x + 2y = 0 + 12

3x + 2y = 12

Put the value of x as 0

3(0) + 2y = 12

0 + 2y = 12

2y = 12

y = 12/2

y = 6

If x = 0. Then, coordinate = (0,6)

Put the value of y as 0

3x + 2(0) = 12

3x + 0 =12

3x = 12

x = 12/3

x = 4

If y = 0. Then, coordinate = (4,0)

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