Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 drag

This system of equations was solved  the Reduction Method:

 Step 1: Multiply the equations by the appropriate numbers (The first equation was multiplied by 5 and the other one bye 7), so that one of the variables disappears by subtracting both equations.

 Step 2: The equations were algebraically added and one of the variables disappeared (Resulting in 31a= 217).

 Step 3: The variable "a" was cleared to know its value (a= 217/31= 7).

 Step 4: The value "a" obtained is substituted in one of the previous equations.

 Step 5: Multiply the 2 (coefficient of "a" in the first equation) by the value "a" obtained (2x7= 14).

 Step 6: The independent term "14" is passed to the right member and his sign changes to negative (-14)

 The final step is to clear variable "b" to know its value (b= -17/4= -2).

Step-by-step explanation: