To solve the system of equations:
- \(10x + 9y = -15\) (Equation 1)
- \(-2x - 2y = 2\) (Equation 2)
Let's first simplify Equation 2. Dividing the entire equation by -2 gives us:
\[ x + y = -1 \quad (Equation 2') \]
Now we can express \(y\) in terms of \(x\) from Equation 2':
\[ y = -1 - x \]
Next, we substitute \(y\) in Equation 1 with \(-1 - x\):
\[ 10x + 9(-1 - x) = -15 \]
Distributing the 9:
\[ 10x - 9 - 9x = -15 \]
Combining like terms:
\[ x - 9 = -15 \]
Adding 9 to both sides gives us:
\[ x = -15 + 9 = -6 \]
Now that we have \(x\), we can find \(y\) using Equation 2':
\[ y = -1 - (-6) = -1 + 6 = 5 \]
So, the solution to the system of equations is:
\[ (x, y) = (-6, 5) \]
The final answer is:
\[ \boxed{(-6, 5)} \]