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

The given equations are

x = 0 …(i)

y = 1 …(ii)

and 2x + y = 2 …(iii)

Let eq. (i), (ii) and (iii) represents the sides AB, BC and AC respectively of ΔABC

From eq. (i) and (ii), we get x = 0 and y = 1

Thus, AB and BC intersect at (0, 1)

Solving eq. (ii) and (iii), we get

y = 1 …(ii)

and 2x + y = 2 …(iii)

Putting the value of y = 1 in eq. (iii), we get

2x + 1 = 2

⇒ 2x = 1

Now, Solving eq. (iii) and (i), we get

2x + y = 2 …(iii)

and x = 0 …(i)

Putting the value of x = 0 in eq. (iii), we get

y = 2

Thus, AC and AB intersect at (0, 2)