1. The problem is to find the solution to the system of equations given by the two lines: Line A: $y=\frac{1}{2}x + 8$ Line B: $y=-2x + 16$ 2. The solution to a system of equations is the point where the two lines intersect, meaning the $x$ and $y$ values satisfy both equations simultaneously. 3. Since the graph shows the lines intersect at $(4,10)$, we verify this by substituting $x=4$ into both equations: For Line A: $$y=\frac{1}{2}(4) + 8 = 2 + 8 = 10$$ For Line B: $$y=-2(4) + 16 = -8 + 16 = 8$$ 4. The calculation for Line B shows $y=8$, which contradicts the graph's intersection point $y=10$. Let's re-check the substitution for Line B: $$y = -2(4) + 16 = -8 + 16 = 8$$ This suggests the graph's intersection point might be incorrect or the equation for Line B might be different. 5. However, the problem states the lines intersect at $(4,10)$, so let's solve the system algebraically to find the exact intersection point. Set the two equations equal: $$\frac{1}{2}x + 8 = -2x + 16$$ 6. Multiply both sides by 2 to eliminate the fraction: $$2 \times \left(\frac{1}{2}x + 8\right) = 2 \times (-2x + 16)$$ $$x + 16 = -4x + 32$$ 7. Add $4x$ to both sides: $$x + 4x + 16 = 32$$ $$5x + 16 = 32$$ 8. Subtract 16 from both sides: $$5x + \cancel{16} - \cancel{16} = 32 - 16$$ $$5x = 16$$ 9. Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{16}{\cancel{5}}$$ $$x = \frac{16}{5} = 3.2$$ 10. Substitute $x=3.2$ into Line A to find $y$: $$y = \frac{1}{2}(3.2) + 8 = 1.6 + 8 = 9.6$$ 11. Substitute $x=3.2$ into Line B to verify $y$: $$y = -2(3.2) + 16 = -6.4 + 16 = 9.6$$ 12. Both lines intersect at $(3.2, 9.6)$. **Final answer:** The solution to the system is $\boxed{(3.2, 9.6)}$.