What is the area of the triangle formed by the lines $2x + y = 8$, $x - y = 1$ and the $y$-axis?

Explanation

1. 01

   The lines meet where $3x = 9$: $x = 3$, $y = 2$.

2. 02

   On the $y$-axis $(x = 0)$ the lines cut at $y = 8$ and $y = -1$, so the base on the axis is $8 - (-1) = 9$.

3. 03

   The height is the distance of $(3, 2)$ from the $y$-axis, which is 3.

4. 04

   Area $= \frac{1}{2} \times 9 \times 3 = \frac{27}{2}$ square units.