1. **State the problem:** Find the solution set of the simultaneous equations by graphical method for the first problem: $$2x + 2 = y$$ $$y = x - 1$$ 2. **Rewrite equations in slope-intercept form:** Equation 1: $$y = 2x + 2$$ Equation 2: $$y = x - 1$$ 3. **Find four ordered pairs for each equation:** For $$y = 2x + 2$$: - When $$x=0$$, $$y=2(0)+2=2$$, so $$(0,2)$$ - When $$x=1$$, $$y=2(1)+2=4$$, so $$(1,4)$$ - When $$x=2$$, $$y=2(2)+2=6$$, so $$(2,6)$$ - When $$x=-1$$, $$y=2(-1)+2=0$$, so $$(-1,0)$$ For $$y = x - 1$$: - When $$x=0$$, $$y=0-1=-1$$, so $$(0,-1)$$ - When $$x=1$$, $$y=1-1=0$$, so $$(1,0)$$ - When $$x=2$$, $$y=2-1=1$$, so $$(2,1)$$ - When $$x=-1$$, $$y=-1-1=-2$$, so $$(-1,-2)$$ 4. **Find the solution by equating the two expressions for $$y$$:** $$2x + 2 = x - 1$$ Subtract $$x$$ from both sides: $$2x + 2 - x = x - 1 - x$$ $$\cancel{2x} + 2 - \cancel{x} = \cancel{x} - 1 - \cancel{x}$$ $$x + 2 = -1$$ Subtract 2 from both sides: $$x + 2 - 2 = -1 - 2$$ $$x = -3$$ Substitute $$x = -3$$ into $$y = x - 1$$: $$y = -3 - 1 = -4$$ 5. **Final solution:** The solution set is $$(-3, -4)$$, the point where the two lines intersect. **Summary:** - Equation 1 points: $$(0,2), (1,4), (2,6), (-1,0)$$ - Equation 2 points: $$(0,-1), (1,0), (2,1), (-1,-2)$$ - Solution: $$(-3,-4)$$ This completes the graphical solution for the first simultaneous equation system.