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Question

The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.

StatementsReasons
2x + 2y = 14	−x + y = 5	Given
2x + 2y = 14	−2x + 2y = 10	?

 

A.Multiplication Property of Equality

 B.Addition Property of Equality 

C.Division Property of Equality 

D.Subtraction Property of Equality

Answer 1

Start with the 2nd given equation

-x + y = 5

Multiply both sides by 2

2*(-x + y) = 2*5

-2x + 2y = 10

As you can see "-x+2y=5" is the same as saying "-2x + 2y = 10". This is due to Multiplication Property of Equality. The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved).