Area of triangle formed by straight lines `4x - y = 4, 3 x + 2y = 14 and `y -axis is

Options

A. `(11)/(2)` sq. unit
B. `(11)/(4)` sq. unit
C. 22 sq. unit
D. 11 sq. unit

Answer

To find the area of the triangle formed by the lines \(4x - y = 4\), \(3x + 2y = 14\), and the y-axis, we will follow these steps:

### Step 1: Find the intercepts of the first line \(4x - y = 4\).

1. **Find the y-intercept**: Set \(x = 0\).
\[ 4(0) - y = 4 \implies -y = 4 \implies y = -4 \]
So, the y-intercept is \((0, -4)\).

2. **Find the x-intercept**: Set \(y = 0\).
\[ 4x - 0 = 4 \implies 4x = 4 \implies x = 1 \]
So, the x-intercept is \((1, 0)\).