To solve the system of equations using substitution, we will substitute the expression for \( y \) from one equation into the other.
We have the two equations:
- \( y = -6x - 3 \)
- \( y = -4x - 5 \)
Since both equations equal \( y \), we can set them equal to each other:
\[ -6x - 3 = -4x - 5 \]
Next, we'll solve for \( x \). First, let’s get all the \( x \) terms on one side by adding \( 6x \) to both sides:
\[ -3 = 2x - 5 \]
Now add \( 5 \) to both sides:
\[ -3 + 5 = 2x \]
This simplifies to:
\[ 2 = 2x \]
Now, divide both sides by \( 2 \):
\[ x = 1 \]
Now that we have the value of \( x \), we will substitute it back into one of the original equations to find \( y \). Let's use the first equation:
\[ y = -6(1) - 3 \] \[ y = -6 - 3 \] \[ y = -9 \]
So, the solution to the system of equations is:
\[ (x, y) = (1, -9) \]
Thus, the final answer is:
\[ (1, -9) \]
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