The system of equations given is:

1. $y = \frac{3}{2}x - 1$
2. $y = -\frac{3}{2}x + 5$

To solve this system of equations, we need to find the point of intersection, which means solving for $x$ and $y$ where both equations are equal.

Step 1: Set the equations equal to each other

Since both expressions represent $y$, we can set them equal to each other:

$\frac{3}{2}x - 1 = -\frac{3}{2}x + 5$

Step 2: Solve for $x$

Now, add $\frac{3}{2}x$ to both sides to eliminate the term from the right side:

$\frac{3}{2}x + \frac{3}{2}x - 1 = 5$

This simplifies to:

$3x - 1 = 5$

Next, add 1 to both sides:

$3x = 6$

Now, divide both sides by 3:

$x = 2$

Step 3: Solve for $y$

Now that we have $x = 2$, substitute it into either of the original equations to find $y$. I'll use the first equation:

$y = \frac{3}{2}(2) - 1$

Simplify:

$y = 3 - 1 = 2$

Final Solution:

The solution to the system of equations is $(x, y) = (2, 2)$.

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

Here are 5 related questions:

1. How do you solve a system of equations graphically?
2. What happens if two equations have no point of intersection?
3. How can you check if two lines are parallel or perpendicular?
4. Can systems of equations have more than one solution?
5. What are some methods other than substitution to solve a system of equations?

Tip: If the slopes of two lines are negative reciprocals, the lines are perpendicular to each other!