Question

Solve for the given replacement set.

A. 6y = 54   {7,8,9}

B. x^2 - x = 3  {1,3,9}

Answer 1

A) The equation is 6y = 54 and replacement set is {7, 8, 9}.

Replace 7 for y.

6(7) ≟ 54

42 ≠ 54

So, 7 is not a solution.

Replace 8 for y.

 6(8) ≟ 54

48 ≠ 54

So, 8 is not a solution.

Replace 8 for y.

 6(9) ≟ 54

54 = 54 True

So, 9 is a solution.

Therefore the solution set is {9}.

B) The equation is x² - x = 3 and replacement set is {1,3,9}.

Replace 1 for x.

(1)² - 1 ≟ 3

1 - 1 ≟ 3

0 ≠ 3

So, 1 is not a solution.

Replace 3 for x.

(3)² - 3 ≟ 3

9 - 3 ≟ 3

6 ≠ 3

So, 3 is not a solution.

Replace 9 for x.

(9)² - 9 ≟ 3

81 - 9 ≟ 3

72 ≠ 3

So, 9 is not a solution.

The replacement set {1,3,9} is not a solution set.

 

Answer 2

(A). The equation is 6y = 54 and the replacement set is {7, 8, 9}.

Replace y in 6y = 54 with each value in the replacement set.

y	6y = 54	True or False?
7		false
8		false
9		true

Since y = 9 makes the equation true, the solution of 6y = 54 is 9.

The solution set is {9}.

(B). The equation is x² - x = 3 and the replacement set is {1, 3, 9}.

Replace x in x² - x = 3 with each value in the replacement set.

x	x2 - x = 3	True or False?
1		false
3		false
9		false

There is no any value of x makes the equation true, in the replacement set..

The solution set is empty set or ∅.

Comments

Typo mistake ----->

In the answer A, the table value at x = 9, 6(9) ≟ 54 → 54 = 54, this is true.