Question

The following proof shows an equlvalent system of equations created from another system of equations. Fll in the missing reason in the proof. Statements Reasons

2x+2Y= 14
-X+y5
2x+2y = 14
-2x + 2y= 10
Given
A Multiplication Property of Equality
B Addition Property of Equality
C Division Property of Equality
D Subtraction Property of Equality

Answer 1

The missing reason in the proof is the Multiplication Property of Equality (A), with a correction in the resulting equation after the multiplication.

Step-by-step explanation:

The subject of this question is to identify the missing reason in a proof relating to a system of linear equations. Given the two initial equations, 2x + 2y = 14 and -x + y = 5, by using the Multiplication Property of Equality, we may continue transforming the second equation to create an equivalent system. The second equation is multiplied by -2 across all terms to get -2x + 2y = -10.

However, there is a mistake in the transformation because -2 multiplied by 5 should result in -10, not 10, as is written in the proof. Therefore, the correct second step should be -2x + 2y = -10 and the reason for this step is indeed the Multiplication Property of Equality (A).