1. **State the problem:** We need to find the solution to the system of equations \(y = x - 2\) and \(y = -x + 4\) and graph them. 2. **Set the equations equal to find the intersection point:** Since both equal \(y\), set \(x - 2 = -x + 4\). 3. **Solve for \(x\):** $$x - 2 = -x + 4$$ $$x + x = 4 + 2$$ $$2x = 6$$ $$x = 3$$ 4. **Find \(y\) by substituting \(x = 3\) into one of the equations:** $$y = 3 - 2 = 1$$ 5. **Solution:** The lines intersect at the point \((3, 1)\). 6. **Graphing:** - The first line \(y = x - 2\) has a slope of 1 and y-intercept at \(-2\). - The second line \(y = -x + 4\) has a slope of -1 and y-intercept at \(4\). These lines cross at \((3, 1)\), which is the solution to the system.