Geometry

Question Analysis:
This question involves identifying when two algebraic expressions are equivalent due to multiplication by a constant.
The main focus is on recognizing redundancy in a system of equations.

Key Concept Explanation:
The Multiplication Property of Equality states that if a = b, then multiplying both sides by the same nonzero constant c results in ac = bc.
In a system of equations, one equation being a multiple of another means they represent the same line, leading to infinite solutions or redundancy.

Step-by-Step Solution:
The first equation is: 3x + 2y = 14
The second equation is: 6x + 4y = 28
If we multiply both sides of the first equation by 2, we obtain:
(3x + 2y) × 2 = 14 × 2
6x + 4y = 28
This confirms that the second equation is simply the first equation multiplied by 2, making it redundant.

Option Analysis:
A) Addition Property of Equality (Incorrect): This property allows adding the same value to both sides of an equation but is not relevant here.
B) Multiplication Property of Equality (Correct): The second equation is a multiple of the first, proving redundancy.
C) Substitution Property (Incorrect): Substitution involves replacing one variable or expression with an equivalent value, which is not needed in this proof.
D) Transitive Property of Equality (Incorrect): This property involves linking multiple equa...