To solve the system of equations using the substitution method, we will start with the two equations:
- \( 2.5x + y = -2 \) (Equation 1)
- \( 3x + 2y = 0 \) (Equation 2)
First, we can solve Equation 1 for \( y \):
\[ y = -2 - 2.5x \]
Now that we have \( y \) in terms of \( x \), we can substitute this expression for \( y \) into Equation 2:
\[ 3x + 2(-2 - 2.5x) = 0 \]
Now simplify:
\[ 3x - 4 - 5x = 0 \]
Combine like terms:
\[ -2x - 4 = 0 \]
Now, solve for \( x \):
\[ -2x = 4 \]
\[ x = -2 \]
Now that we have \( x \), we can substitute it back into the expression we found earlier for \( y \):
\[ y = -2 - 2.5(-2) \]
Calculate \( y \):
\[ y = -2 + 5 = 3 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-2, 3) \]
So the correct response is:
(−2, 3)