1. **State the problem:** We are given two equations: $$x + y = 4$$ $$y = 2x - 5$$ We need to draw their graphs and find the coordinates of the point satisfying both equations. 2. **Rewrite equations for graphing:** For $$x + y = 4$$, express $$y$$ as $$y = 4 - x$$. 3. **Select points to graph $$y = 4 - x$$:** If $$x = 0, y = 4 - 0 = 4$$ If $$x = 4, y = 4 - 4 = 0$$ 4. **Select points to graph $$y = 2x - 5$$:** If $$x = 0, y = 2(0) - 5 = -5$$ If $$x = 5, y = 2(5) - 5 = 10 - 5 = 5$$ 5. **Use the scale 2 cm to 1 unit to draw the axes and plot these points:** Plot points (0,4) and (4,0) for the first line. Plot points (0,-5) and (5,5) for the second line. Draw straight lines through these points for each equation. 6. **Find the intersection algebraically to confirm:** From $$y = 4 - x$$ and $$y = 2x - 5$$, set equal: $$4 - x = 2x - 5$$ $$4 + 5 = 2x + x$$ $$9 = 3x$$ $$x = 3$$ 7. **Find corresponding $$y$$ value:** $$y = 4 - 3 = 1$$ or $$y = 2(3) - 5 = 6 - 5 = 1$$ 8. **Answer:** The coordinates satisfying both equations are: $$(3, 1)$$