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 = 14y = x + 5 ?

A.) Multiplication Property of Equality

B.) Addition Property of Equality

C.) Division Property of Equality

D.) Subtraction Property of Equality

Answer 1

Addition property of equality

Explanation:

Given:

`2x+2y=14 \ -x+y = 5`

We need to find the missing reason in the proof.

Solution:

By solving the above equation we get;

`2x+2y=14 \ -x+y = 5` ⇒ Given:

Now by adding both side by 'x' we get;

`2x+2y=14 \ -x+y+x = 5+x`

`2x+2y=14 \ y = x+5` ⇒ Addition property of equality

Hence The missing reason in the proof was Addition Property of equality.