1. **State the problem:** We are given two linear equations: $$-10x + 3y = 34$$ $$y = -8x$$ We want to find the solution to this system of equations, which is the point where the two lines intersect. 2. **Substitute the expression for $y$ from the second equation into the first:** $$-10x + 3(-8x) = 34$$ 3. **Simplify the equation:** $$-10x - 24x = 34$$ $$-34x = 34$$ 4. **Solve for $x$ by dividing both sides by $-34$:** $$x = \frac{34}{\cancel{-34}}\cancel{-1} = -1$$ 5. **Substitute $x = -1$ back into the second equation to find $y$:** $$y = -8(-1) = 8$$ 6. **Final answer:** The solution to the system is the point where the two lines intersect: $$\boxed{(-1, 8)}$$