To solve the system of equations given by \( y = -\frac{3}{2}x - 2 \) and \( 2x - y = -5 \), we can use substitution or elimination. Here, I will use substitution.
We already have \( y \) expressed from the first equation: \[ y = -\frac{3}{2}x - 2 \]
Now, we will substitute this expression for \( y \) into the second equation \( 2x - y = -5 \): \[ 2x - \left(-\frac{3}{2}x - 2\right) = -5 \]
This simplifies to: \[ 2x + \frac{3}{2}x + 2 = -5 \]
Next, combine the \( x \) terms: \[ 2x + \frac{3}{2}x = \frac{4}{2}x + \frac{3}{2}x = \frac{7}{2}x \]
So we have: \[ \frac{7}{2}x + 2 = -5 \]
Now, isolate the term with \( x \): \[ \frac{7}{2}x = -5 - 2 \] \[ \frac{7}{2}x = -7 \]
Now multiply both sides by \( \frac{2}{7} \): \[ x = -7 \times \frac{2}{7} = -2 \]
Now that we have \( x \), we can substitute back to find \( y \): \[ y = -\frac{3}{2}(-2) - 2 \] \[ y = 3 - 2 = 1 \]
Therefore, the solution to the system of equations is: \[ (x, y) = (-2, 1) \]
To summarize, the solution is: \[ \boxed{(-2, 1)} \]