Solve the following system of equations. \[ \begin{aligned}-4 x+y & =13 \\ 5 x+y & =-14\end{aligned} \]

To solve the given system of equations: 1. Start with the two equations: \[ \begin{aligned} -4x + y & = 13 \quad \text{(1)} \\ 5x + y & = -14 \quad \text{(2)} \end{aligned} \] 2. We can eliminate \(y\) by subtracting equation (1) from equation (2). This gives us: \[ (5x + y) - (-4x + y) = -14 - 13 \] Simplifying this, we get: \[ 5x + y + 4x - y = -27 \implies 9x = -27 \] 3. Now, solve for \(x\): \[ x = -3 \] 4. Substitute \(x = -3\) back into either original equation to find \(y\). We'll use equation (1): \[ -4(-3) + y = 13 \] \[ 12 + y = 13 \implies y = 1 \] 5. Thus, the solution to the system of equations is: \[ x = -3, \quad y = 1 \] The solution can be expressed as the ordered pair: \[ (-3, 1) \]