To solve this graphically:

The given equations are:

1. $y = 2x - 2$
2. $y = x + 1$

Steps to solve:

1. Plot both equations on the graph:

   • For $y = 2x - 2$:
     • When $x = 0$, $y = -2$ (point $(0, -2)$).
     • When $x = 2$, $y = 2$ (point $(2, 2)$).
   • For $y = x + 1$:
     • When $x = 0$, $y = 1$ (point $(0, 1)$).
     • When $x = 2$, $y = 3$ (point $(2, 3)$).

2. Find the point of intersection:

   • From the graph provided, the two lines intersect at $x = 3$. Substituting $x = 3$ into either equation:
     • $y = 2(3) - 2 = 6 - 2 = 4$ (for the first equation).
     • $y = 3 + 1 = 4$ (for the second equation).

Thus, the solution is $x = 3$ and $y = 4$.

Let me know if you want further details or have any questions!

Related Questions:

1. How would you verify the solution algebraically?
2. What are other methods to solve simultaneous equations besides graphing?
3. Can simultaneous equations always have solutions?
4. What happens if the lines are parallel when solving graphically?
5. How can you solve these equations using substitution?

Tip:

Always verify graphically obtained solutions algebraically for confirmation!