Question

Complete the two-column proof.

Answer 1

88 - 6y = -1       substitution property (as 8 is substituted to replace x)
-6y = -89           subtraction property (88 is subtracted to the whole eqn)
y = 89/6            division property (-6 is the divisor)
89/6 = y            transitive property (exchange of places results to the same value)

Answer 2

The correct answers are:

substitution property; subtraction property of equality; division property of equality; and reflexive property.

Explanation:

The difference between the given statement and the first statement is that 11x is replaced with 88.  This is because we are told that x=8; 11(8) = 88.  Substitution has been used here.

The difference between the first step and the second step is that 88 is no longer on the left hand side and the right hand side is -89.  This is because to cancel 88, it has been subtracted from each side of the equation.  This is the subtraction property of equality.

The difference between the second step and the third step is that -6 is no longer on the left side and the right hand side is 89/6.  This is because to cancel -6 both sides were divided by -6.  This is the division property of equality.

The difference between the third step and the last step is that the 89/6 and y have been flipped around the equals sign.  This is the reflexive property.