To solve the system of equations using the substitution method, we'll start with the given equations:
- \(2.5x + y = -2\)
- \(3x + 2y = 0\)
Step 1: Solve one of the equations for one variable.
We'll solve the first equation for \(y\):
\[ y = -2 - 2.5x \]
Step 2: Substitute this expression for \(y\) into the second equation.
Substituting \(y\) in the second equation:
\[ 3x + 2(-2 - 2.5x) = 0 \]
Step 3: Simplify and solve for \(x\).
This simplifies to:
\[ 3x - 4 - 5x = 0 \]
Combining like terms gives:
\[ -2x - 4 = 0 \]
Solving for \(x\):
\[ -2x = 4 \implies x = -2 \]
Step 4: Substitute \(x\) back into the expression for \(y\).
Now substitute \(x = -2\) back into the equation we found for \(y\):
\[ y = -2 - 2.5(-2) \]
Calculating this gives:
\[ y = -2 + 5 = 3 \]
Step 5: Write the solution as an ordered pair.
Thus, the solution to the system of equations is:
\[ (x, y) = (-2, 3) \]
Final Answer:
The solution is \((-2, 3)\).