1. **State the problem:** We are given the system of linear equations: $$3x - 4y = 7$$ $$2x + y = -10$$ We need to find the value of $x - y$ for the solution $(x,y)$ of this system. 2. **Use substitution or elimination method:** Here, we will use substitution. From the second equation, solve for $y$: $$y = -10 - 2x$$ 3. **Substitute $y$ into the first equation:** $$3x - 4(-10 - 2x) = 7$$ Simplify: $$3x + 40 + 8x = 7$$ $$11x + 40 = 7$$ 4. **Solve for $x$:** $$11x = 7 - 40$$ $$11x = -33$$ $$x = -3$$ 5. **Find $y$ using $x = -3$:** $$y = -10 - 2(-3) = -10 + 6 = -4$$ 6. **Calculate $x - y$:** $$x - y = -3 - (-4) = -3 + 4 = 1$$ **Final answer:** $$\boxed{1}$$