To solve the system of equations:
- \(-8x + 7y = 18\) (Equation 1)
- \(3x - y = -10\) (Equation 2)
We can use the substitution or elimination method. Here, I'll use substitution. First, we solve Equation 2 for \(y\):
\[ y = 3x + 10 \]
Now, substitute \(y\) in Equation 1:
\[ -8x + 7(3x + 10) = 18 \]
Distributing \(7\):
\[ -8x + 21x + 70 = 18 \]
Combine like terms:
\[ 13x + 70 = 18 \]
Now, isolate \(x\) by subtracting \(70\) from both sides:
\[ 13x = 18 - 70 \] \[ 13x = -52 \]
Now, divide by \(13\):
\[ x = -4 \]
Next, substitute \(x = -4\) back into the expression for \(y\):
\[ y = 3(-4) + 10 \] \[ y = -12 + 10 \] \[ y = -2 \]
Thus, the solution to the system of equations is:
\[ x = -4, \quad y = -2 \]
We can write the solution as \((-4, -2)\).