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
y = x + 5 ?

Answer 1

Answer:

As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.

Step-by-step explanation:

$2x + 2y = 14$

$-x + y = 5$    Add x in both sides (Addition Property of Equality)

$2x + 2y = 14$

$y = x + 5$    Multiply both sides by 2

$2x + 2y = 14$

$2y = 2x + 10$    Subtract 2x in both sides

$+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.$       ∵adding both equation

$4y = 24$ divide both sides by 4

$y = 6$

Put the value of y = 6 to the equation $-x + y = 5$

$-x + 6 = 5$  Subtract 6 from both sides

$-x = -1$    Change the sign

$x = 1$     

Keywords: Addition property of equality, reason, proof

Learn more about operations from brainly.com/question/3474035

#learnwithBrainly