Question

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

Statements Reasons
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
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Answer 1

Answer: Its Multiplication property of Equality

Step-by-step explanation: Just did the test

Answer 2

A.Multiplication Property of Equality

Explanation:

`\left\{\begin{array}{ccc}2x+2y=14\\-x+y=5&\text{\underline{multiply both sides by 2}}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}2x+2y=14\\-2x+2y=10\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=24\qquad\text{divide both sides by 4}\\.\qquad\qquad y=6\\\\\text{put the value of y to the second equation:}\\\\-x+6=5\qquad\text{subtract 6 from both sides}\\-x=-1\qquad\text{change the signs}\\x=1`