Solve the system of equations: $$2x - 3y = 5$$ $$x - 6y = -2$$

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: $$x = 6y - 2$$
2. Substitute this expression for x into the first equation: $$2(6y - 2) - 3y = 5$$
3. Simplify and solve for y: $$12y - 4 - 3y = 5$$ $$9y - 4 = 5$$ $$9y = 9$$ $$y = 1$$
4. Substitute the value of y back into the expression for x: $$x = 6(1) - 2$$ $$x = 6 - 2$$ $$x = 4$$

Answer: $$x=4, y=1$$