Name the property of equality or congruence that justifies going from the first statement to the second statement.

The property of equality that justifies going from the first statement to the second statement  is;

Subtraction property of equality

Step-by-step explanation:

The given equation is presented here as follows;

AB + BC = 42

AB = 42 - BC

The above equation can be simplified as follows;

AB + BC = 42

AB + BC - BC = 42 - BC

(+ BC - BC = 0)

Therefore, we have;

AB + BC - BC = AB + 0 = AB = 42 - BC

AB = 42 - BC  which is the subtraction property of equality

For the subtraction property of equality, when we subtract a value from one side of the equation, we must subtract the same value from the side of the equation as follows

Given that the letters a, b, and c represent any numbers

When we have;

a = b

Then we also must have;

a - c = b - c