Find the point of intersection and the inclination of the two lines
`Ax + By = A + B and A(x- y) + B(x+ y)= 2B`.

Answer

To solve the problem of finding the point of intersection and the inclination of the two lines given by the equations \( Ax + By = A + B \) and \( A(x - y) + B(x + y) = 2B \), we will follow these steps:

### Step 1: Rewrite the equations in standard form

1. **First Line**:
The equation \( Ax + By = A + B \) can be rearranged to:
\[ Ax + By - (A + B) = 0 \]
This gives us the first line \( L_1: Ax + By - A - B = 0 \).

2. **Second Line**:
The equation \( A(x - y) + B(x + y) = 2B \) can be expanded and rearranged:
\[ Ax - Ay + Bx + By = 2B \]
Combining like terms, we have:
\[ (A + B)x + (-A + B)y - 2B = 0 \]
This gives us the second line \( L_2: (A + B)x + (-A + B)y - 2B = 0 \).