To solve the system of equations:
\[ \begin{aligned} & -4x + 7y = 20 \quad \text{(1)} \ & y = 3x + 15 \quad \text{(2)} \end{aligned} \]
we will substitute equation (2) into equation (1).
From equation (2), we have:
\[ y = 3x + 15 \]
Now, substitute \(y\) in equation (1):
\[ -4x + 7(3x + 15) = 20 \]
Expanding this gives:
\[ -4x + 21x + 105 = 20 \]
Combining like terms:
\[ 17x + 105 = 20 \]
Now, isolate \(x\) by subtracting 105 from both sides:
\[ 17x = 20 - 105 \] \[ 17x = -85 \]
Dividing both sides by 17:
\[ x = -5 \]
Now, substitute \(x = -5\) back into equation (2) to find \(y\):
\[ y = 3(-5) + 15 \] \[ y = -15 + 15 \] \[ y = 0 \]
Thus, the solution of the system of equations is:
\[ x = -5 \] \[ y = 0 \]