To solve the system of equations:
- \(-7x - 10y = 20\) (Equation 1)
- \(-x + y = -19\) (Equation 2)
We can use the substitution or elimination method. Here, I will use the substitution method:
First, solve Equation 2 for \(y\):
\[ -y = -x - 19 \implies y = x - 19 \]
Now, substitute \(y\) in Equation 1:
\[ -7x - 10(x - 19) = 20 \]
Now, distribute \(-10\):
\[ -7x - 10x + 190 = 20 \]
Combine like terms:
\[ -17x + 190 = 20 \]
Next, isolate \(x\):
\[ -17x = 20 - 190 \] \[ -17x = -170 \] \[ x = \frac{-170}{-17} = 10 \]
Now, substitute \(x = 10\) back into \(y = x - 19\):
\[ y = 10 - 19 = -9 \]
Thus, the solution to the system of equations is:
\[ x = 10, \quad y = -9 \]
To summarize, the solution is \((10, -9)\).