To solve the system of equations using the substitution method, we'll start with the given equations:
- \( 2.5x + y = -2 \) (Equation 1)
- \( 3x + 2y = 0 \) (Equation 2)
Step 1: Solve one of the equations for one variable.
Let's solve Equation 1 for \( y \):
\[ y = -2 - 2.5x \]
Step 2: Substitute this expression for \( y \) into Equation 2.
Now substitute \( y \) in Equation 2:
\[ 3x + 2(-2 - 2.5x) = 0 \]
Distributing the \( 2 \):
\[ 3x - 4 - 5x = 0 \]
Combine like terms:
\[ -2x - 4 = 0 \]
Step 3: Solve for \( x \)
Add \( 4 \) to both sides:
\[ -2x = 4 \]
Divide by \(-2\):
\[ x = -2 \]
Step 4: Substitute \( x \) back to find \( y \)
Now substitute \( x = -2 \) back into the equation we derived for \( y \):
\[ y = -2 - 2.5(-2) \] \[ y = -2 + 5 = 3 \]
Step 5: Solution
So the solution to the system is:
\[ (x, y) = (-2, 3) \]
Thus, the answer is: \(\boxed{(-2, 3)}\).