To solve the system of equations:
- \( -8x - 5y = 8 \)
- \( x + 3y = 18 \)
we can use the substitution or elimination method. Here, I'll use the elimination method.
First, let's rearrange the second equation to express \(x\) in terms of \(y\):
From equation 2: \[ x = 18 - 3y \]
Now we will substitute \(x\) from this equation into the first equation:
Substituting into equation 1: \[ -8(18 - 3y) - 5y = 8 \]
Now distribute \(-8\): \[ -144 + 24y - 5y = 8 \]
Combine like terms: \[ -144 + 19y = 8 \]
Add \(144\) to both sides: \[ 19y = 152 \]
Now, divide by \(19\): \[ y = 8 \]
Now that we have \(y\), substitute it back into the equation \(x = 18 - 3y\) to find \(x\): \[ x = 18 - 3(8) = 18 - 24 = -6 \]
Thus, the solution to the system of equations is: \[ x = -6, \quad y = 8 \]
The solution can be written as the point \((-6, 8)\).