To solve the system of equations using substitution, we have the following two equations:
- \( y = -3x - 5 \) (Equation 1)
- \( y = -2x - 1 \) (Equation 2)
Since both equations are equal to \( y \), we can set them equal to each other:
\[ -3x - 5 = -2x - 1 \]
Next, we'll solve for \( x \):
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Add \( 3x \) to both sides: \[ -5 = x - 1 \]
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Add \( 1 \) to both sides: \[ -5 + 1 = x \] \[ -4 = x \]
Now that we have \( x = -4 \), we can substitute this value back into either Equation 1 or Equation 2 to find \( y \). We'll use Equation 1:
\[ y = -3(-4) - 5 \] \[ y = 12 - 5 \] \[ y = 7 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, 7) \]
To verify, we can also substitute \( x = -4 \) into Equation 2:
\[ y = -2(-4) - 1 \] \[ y = 8 - 1 \] \[ y = 7 \]
Both equations give us the same result. Therefore, the solution is correct:
\[ \boxed{(-4, 7)} \]