Which properties justify the steps taken to solve the system? {3x−2y=10 4x−3y=14

The answer is: Substitution property of equality.

 The explanation is shown below:

1. To solve this problem you must apply the proccedure shown below:

 2. When you clear the variable x from the first equation, and subtitute it into the second equation, you obtain:

 3x−2y=10
 x=(10+2y)/3

 4x−3y=14
 4[(10+2y)/]−3y=14
 y=-2

 3. When you subsitute y=-2 into the first equation and clear the x, you have:

 x=2