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The system of equations given is:

\[
y = 3x + 1
\]
\[
y = 2x + 2
\]

We can solve this system by substitution or elimination. Let's use the substitution method:

### Step 1: Set the two equations equal to each other.
Since both equations are equal to \(y\), we can equate the right-hand sides:

\[
3x + 1 = 2x + 2
\]

### Step 2: Solve for \(x\).
Subtract \(2x\) from both sides:

\[
x + 1 = 2
\]

Now subtract 1 from both sides:

\[
x = 1
\]

### Step 3: Substitute \(x = 1\) into one of the original equations to find \(y\).
Substitute into the first equation:

\[
y = 3(1) + 1 = 3 + 1 = 4
\]

So, the solution to the system is \(x = 1\) and \(y = 4\), or the point \((1, 4)\).

The correct answer is the fourth option: \((1, 4)\).

---

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the elimination method for solving systems of equations?
2. Can a system of linear equations have no solution?
3. How do you graphically interpret the solution to a system of linear equations?
4. What happens when both equations in a system represent the same line?
5. How do you solve systems of equations with more than two variables?

**Tip:** When solving a system of equations, always double-check your solution by substituting both variables back into the original equations.

Solve the system:

y = 3x + 1
y = 2x + 2

Options:
1. (0, 1)
2. (2, 7)
3. (-2, -5)
4. (1, 4)

Learn how to solve the system of linear equations y = 3x + 1 and y = 2x + 2 by substitution. This algebra problem demonstrates the method of setting equations equal to find the solution, suitable for Grades 8-10.

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