Final answer:
To solve the system by elimination, adding the equations together adheres to the addition property of equality, ensuring the system remains balanced after the operation.
Step-by-step explanation:
When beginning to solve the system of linear equations by elimination, the step of adding the equations together utilizes the D. addition property of equality. The addition property of equality states that if the same amount is added to both sides of an equation, the equality is still balanced.
Therefore, when you add 3x + 2y to 5x - 2y, you are maintaining the equality of both equations because you're performing the same operation to both sides of the equation (3x + 2y = -38 and 5x - 2y = -30) to eliminate one of the variables and simplify the system. The next steps would involve solving for the remaining variable and back-substituting to find the value of the eliminated variable.