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 = 14−4x + 6y = 12Given2x + 2y = 14−2x + 3y = 6?

Answer 1

Division Property of Equality

Explanation:

Answer 2

Equation 2 of system divided by 2 on both sides then we get second equation of system 2.

Explanation:

We are given two equations

`2x+2y=14`

`-4x+6y=12`

We are given a proof which shows an equivalent system of equations created from another system of equations

We have to fill the correct reason in the blank space

Statement:
`2x=2y=14`

`-4x+6y=12`

Reason: Given

Statement :
`2x=2y=14`

`-2x+3y=6`

Reason : equation 2 of system I divided by 2 on both sides then we get second equation of system 2.

When we divide by 2 then the solution does not change and x and y - intercepts are not change.So, the two systems are equivalent.