Solve the system of equations: $$5x - 4y = 12$$ $$x - 5y = -6$$

Solution:

We can solve this system of equations using the substitution method.

1. From the second equation, we can express x in terms of y: $$x = 5y - 6$$
2. Substitute this expression for x into the first equation: $$5(5y - 6) - 4y = 12$$
3. Simplify and solve for y: $$25y - 30 - 4y = 12$$ $$21y - 30 = 12$$ $$21y = 42$$ $$y = 2$$
4. Substitute the value of y back into the expression for x: $$x = 5(2) - 6$$ $$x = 10 - 6$$ $$x = 4$$

Answer: $$x=4, y=2$$