To solve the system of equations given by:
- \( -3x - 10 = y \)
- \( -x - 8y = 11 \)
we can use substitution or elimination. Here, we'll use substitution.
Step 1: Substitute \( y \) from the first equation into the second equation.
From the first equation, we can express \( y \) in terms of \( x \):
\[ y = -3x - 10 \]
Now, we'll substitute this expression for \( y \) into the second equation:
\[ -x - 8(-3x - 10) = 11 \]
Step 2: Solve for \( x \).
Expanding the second equation gives:
\[ -x + 24x + 80 = 11 \]
Combine like terms:
\[ 23x + 80 = 11 \]
Now, isolate \( x \):
\[ 23x = 11 - 80 \] \[ 23x = -69 \] \[ x = -3 \]
Step 3: Substitute \( x \) back to find \( y \).
Now, substitute \( x = -3 \) back into the expression for \( y \):
\[ y = -3(-3) - 10 \]
Calculate \( y \):
\[ y = 9 - 10 \] \[ y = -1 \]
Solution
The solution to the system of equations is:
\[ x = -3, \quad y = -1 \]
Thus, the solution in ordered pair form is:
\[ (-3, -1) \]