1. **State the problem:** We are given the system of equations: $$2x + y = 6$$ $$y = -2x + 6$$ We need to determine which statements about this system are true. 2. **Rewrite the first equation:** Solve the first equation for $y$ to compare with the second. $$2x + y = 6 \implies y = 6 - 2x$$ 3. **Compare the two equations:** The second equation is $$y = -2x + 6$$ Notice that $6 - 2x$ and $-2x + 6$ are equivalent expressions (commutative property of addition). 4. **Interpretation:** Both equations represent the same line because they have the same slope ($-2$) and the same y-intercept ($6$). 5. **Check the statements:** - A) The system has no solution. **False** because the lines are the same. - B) The system has infinitely many solutions. **True** because the lines coincide. - C) The two equations represent the same line. **True** as shown. - D) The graphs of the lines are parallel and never intersect. **False** because they are the same line, not just parallel. - E) The point $(2, 2)$ is a solution to the system. Check by substituting: $$2x + y = 6 \implies 2(2) + 2 = 4 + 2 = 6$$ $$y = -2x + 6 \implies 2 = -2(2) + 6 = -4 + 6 = 2$$ Both true, so **True**. **Final answers:** B, C, and E are true.