The problem involves a system of linear equations with four unknowns: A, B, C, and D. We are given two equations, and we are required to solve the system using the provided equations. Equation 1: $A + B + 2C + D = -6$ Equation 2: $3A - B - C + D = -11$

1. Problem Description

The problem involves a system of linear equations with four unknowns: A, B, C, and D. We are given two equations, and we are required to solve the system using the provided equations.

Equation 1: $A + B + 2C + D = -6$

Equation 2: $3A - B - C + D = -11$

2. Solution Steps

We are given the following equations:

Equation (1): $A + B + 2C + D = -6$

Equation (2): $3A - B - C + D = -11$

We can eliminate B by adding Equation (1) and Equation (2):

$(A + B + 2C + D) + (3A - B - C + D) = -6 + (-11)$

$4A + C + 2D = -17$

Let's call this Equation (3):

$4A + C + 2D = -17$

3. Final Answer

$4A + C + 2D = -17$