501. Solve the system of equations: 4x - 3y = -1, x - 5y = 4.

Solution:

1. Multiply the second equation by 5: 5(x - 5y) = 5(4) => 5x - 25y = 20.
2. Subtract the first equation from the modified second equation: (5x - 25y) - (4x - 3y) = 20 - (-1) => 5x - 25y - 4x + 3y = 21 => x - 22y = 21.
3. From the original second equation, express x: x = 4 + 5y.
4. Substitute this expression for x into the equation from step 2: (4 + 5y) - 22y = 21 => 4 - 17y = 21 => -17y = 17 => y = -1.
5. Substitute the value of y back into the equation for x: x = 4 + 5(-1) = 4 - 5 = -1.

Answer: x = -1, y = -1