506. Solve the system of equations: 5x - 4y = 12, x - 5y = -6.

Solution:

1. From the second equation, express x: x = 5y - 6.
2. Substitute this expression for x into the first equation: 5(5y - 6) - 4y = 12 => 25y - 30 - 4y = 12 => 21y = 42 => y = 2.
3. Substitute the value of y back into the equation for x: x = 5(2) - 6 = 10 - 6 = 4.

Answer: x = 4, y = 2