To solve the system of equations using the substitution method, we first need to solve one of the equations for one variable and then substitute that expression into the other equation. Let's start with the first equation:
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First equation:
\[ 2.5x + y = -2 \]We can solve for \( y \): \[ y = -2 - 2.5x \]
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Second equation:
\[ 3x + 2y = 0 \]Now we'll substitute the expression for \( y \) from the first equation into the second equation. Replace \( y \) in the second equation: \[ 3x + 2(-2 - 2.5x) = 0 \]
Now simplify this equation: \[ 3x - 4 - 5x = 0 \] Combine like terms: \[ -2x - 4 = 0 \]
Add 4 to both sides: \[ -2x = 4 \]
Now divide by -2: \[ x = -2 \]
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Substitute \( x \) back into the expression for \( y \):
Now we use the value of \( x \) to find \( y \). Substitute \( x = -2 \) into the equation we found for \( y \): \[ y = -2 - 2.5(-2) \] Calculate \( y \): \[ y = -2 + 5 = 3 \]
Thus, the solution to the system of equations is: \[ x = -2, \quad y = 3 \]
The solution can be written as the ordered pair: \[ \boxed{(-2, 3)} \]