1. **State the problem:** We need to find the solution to the system of equations: $$y = -2x + 7$$ $$y = x + 1$$ This means finding the point $(x,y)$ where the two lines intersect. 2. **Set the equations equal:** Since both expressions equal $y$, set them equal to each other: $$-2x + 7 = x + 1$$ 3. **Solve for $x$:** Add $2x$ to both sides: $$\cancel{-2x} + 7 + 2x = x + 1 + 2x$$ $$7 = 3x + 1$$ Subtract 1 from both sides: $$7 - 1 = 3x + \cancel{1} - 1$$ $$6 = 3x$$ Divide both sides by 3: $$\frac{6}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$2 = x$$ 4. **Find $y$:** Substitute $x=2$ into one of the original equations, for example $y = x + 1$: $$y = 2 + 1 = 3$$ 5. **Solution:** The coordinates of the solution are: $$(2, 3)$$ This is the point where the two lines intersect on the graph.