Finding Integer Solutions for Linear Equations and Inequalities

Consider the system of linear equations:

$$3x + 2y = 12$$

$$4x - y = 1$$

Find the value of $$x$$ such that the solution to the system satisfies the inequalities:

$$x + 2y < 10$$

$$x - y > -1$$

Determine the number of integer values of $$x$$ that satisfy these conditions.