To solve the system of equations using the substitution method, we start with the given equations:
- \( 2.5x + y = -2 \) (Equation 1)
- \( 3x + 2y = 0 \) (Equation 2)
Step 1: Solve one equation for one variable
We can solve Equation 1 for \( y \):
\[ y = -2 - 2.5x \]
Step 2: Substitute into the other equation
Now we'll substitute \( y \) into Equation 2:
\[ 3x + 2(-2 - 2.5x) = 0 \]
Expanding this gives:
\[ 3x - 4 - 5x = 0 \]
Step 3: Combine like terms
Combine the \( x \) terms:
\[ 3x - 5x - 4 = 0 \] \[ -2x - 4 = 0 \]
Step 4: Solve for \( x \)
Adding 4 to both sides:
\[ -2x = 4 \]
Now divide by -2:
\[ x = -2 \]
Step 5: Substitute back to find \( y \)
Now substitute \( x = -2 \) back into the equation we found for \( y \):
\[ y = -2 - 2.5(-2) \] \[ y = -2 + 5 = 3 \]
Thus, we have \( x = -2 \) and \( y = 3 \).
Final Solution
The solution to the system is:
\[ (-2, 3) \]
Thus, the correct answer is:
(−2, 3) (left parenthesis negative 2 comma 3 right parenthesis).
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