Draw the graph of the pair of equations `x - 2y =4 and 3x + 5y =1.` Write the verticves of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Answer

To solve the problem step by step, we will first plot the graphs of the given equations, find the vertices of the triangle formed by the lines and the y-axis, and then calculate the area of that triangle.

### Step 1: Rewrite the equations in slope-intercept form
1. **Equation 1:** \( x - 2y = 4 \)
- Rearranging gives:
\[ 2y = x - 4 \implies y = \frac{1}{2}x - 2 \]

2. **Equation 2:** \( 3x + 5y = 1 \)
- Rearranging gives:
\[ 5y = 1 - 3x \implies y = -\frac{3}{5}x + \frac{1}{5} \]