Find the area of the triangle formed by the lines 2x+3y=12, x-y-1=0 and x=0.

The given pair of linear equations are:

2 x + 3 y = 12

x - y - 1 = 0

x = 0

Plot the graph of the line

2 x + 3 y = 12

using the table below:

So, the coordinates of the line equation

2 x + 3 y = 12

are

(0, 4)

.
Plot the graph of the line

x - y - 1 = 0

using the table below:

So, the coordinates of the line equation

x - y - 1 = 0

are

(0, - 1)

.
Plot the graph of the line

x = 0

.
The graph of lines is

From the graph, in

ΔABC

Height of the triangle

= 3 units

Base of the triangle

= 5 units

Area of the triangle

= \frac{1}{2} \times B \times H

\Rightarrow \frac{1}{2} \times 5 \times 3

\Rightarrow 7.5 square units

Therefore, the area of the triangle is 7.5 square units.
Hence, option 2 is correct.

Find the area of the triangle formed by the lines $2 x + 3 y = 12$ , $x - y - 1 = 0$ and $x = 0$ .