Let's solve the system of equations step-by-step to find which point satisfies both equations.

The system of equations:

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

Step 1: Set the two equations equal to each other

Since both expressions are equal to $y$, we can set the right-hand sides equal to each other:

$2x - 2 = x + 2$

Step 2: Solve for $x$

First, subtract $x$ from both sides:

$2x - x - 2 = 2$ $x - 2 = 2$

Now, add 2 to both sides:

$x = 4$

Step 3: Solve for $y$

Now that we know $x = 4$, substitute $x = 4$ into one of the original equations. Let's use the second equation $y = x + 2$:

$y = 4 + 2 = 6$

Step 4: Check the result

The solution is $x = 4$ and $y = 6$, so the point $(4, 6)$ should be a solution to the system.

Step 5: Verify with the first equation

Substitute $x = 4$ into the first equation $y = 2x - 2$:

$y = 2(4) - 2 = 8 - 2 = 6$

Thus, the point $(4, 6)$ satisfies both equations.

Answer:

The correct point is D. (4, 6).

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Would you like to explore more details about solving systems of equations or have any other questions?

Related questions:

1. How do you solve a system of equations using substitution?
2. How would you solve this system using elimination?
3. What is the graphical interpretation of solving a system of equations?
4. How can you check the solution of a system using graphing?
5. What would happen if the system has no solution or infinitely many solutions?

Tip: When solving a system of equations, it's often useful to graph both equations to visually see where they intersect.