Area of triangle formed by straight line `2x + 3y = 5 and y = 3x - 13` with x-axis is

Options

A. `(11)/(3)` sq. unit
B. `(22)/(3)` sq. unit
C. `(11)/(6) ` sq. unit
D. `(11)/(12)` sq. unit

Answer

To find the area of the triangle formed by the lines \(2x + 3y = 5\) and \(y = 3x - 13\) with the x-axis, we will follow these steps:

### Step 1: Find the x-intercept and y-intercept of the first line \(2x + 3y = 5\).

1. **To find the x-intercept**, set \(y = 0\):
\[ 2x + 3(0) = 5 \implies 2x = 5 \implies x = \frac{5}{2} \]
So, the x-intercept is \(\left(\frac{5}{2}, 0\right)\).

2. **To find the y-intercept**, set \(x = 0\):
\[ 2(0) + 3y = 5 \implies 3y = 5 \implies y = \frac{5}{3} \]
So, the y-intercept is \(\left(0, \frac{5}{3}\right)\).