To determine if the pair \((-8, -2)\) is a solution to the system of equations, you need to check if it satisfies both equations.
The equations are:
- \( y = \frac{1}{2}x + 2 \)
- \( y = -2 \)
First, substitute \(x = -8\) and \(y = -2\) into the first equation:
\[ y = \frac{1}{2}(-8) + 2 \]
Calculating the right side:
\[ y = -4 + 2 = -2 \]
Since both sides of the equation are equal (\(-2 = -2\)), the first equation is satisfied.
Next, check the second equation with \(y = -2\):
\[ y = -2 \]
This is also satisfied.
Since \((-8, -2)\) satisfies both equations, it is indeed a solution to the system of equations.