Answer:
The accepted y-values are:
4, 0, -2, 6 and -13
Explanation:
We are looking for the values that satisfy either the first inequality, the second inequality or both.
Therefore, to get the y-values that belong to the solution set, we will simply substitute with the given values in both inequalities. The ones that satisfy at least one inequality will be accepted. If a value of y does not satisfy any of the two inequalities, then it will be rejected
This is done as follows:
a. At y = 4:
Inequality 1 .........> -4y + 9 = -4(4) + 9 = -7 which is not greater than 37
Inequality 2 ........> 3y - 11 = 3(4) - 11 = 1 which is greater than -17
The second inequality is satisfied, therefore, 4 belongs to the solution set
b. At y = 0:
Inequality 1 .........> -4y + 9 = -4(0) + 9 = 9 which is not greater than 37
Inequality 2 ........> 3y - 11 = 3(0) - 11 = -11 which is greater than -17
The second inequality is satisfied, therefore, 0 belongs to the solution set
c. At y = -2:
Inequality 1 .........> -4y + 9 = -4(-2) + 9 = 17 which is not greater than 37
Inequality 2 ........> 3y - 11 = 3(-2) - 11 = -17 which is equal to -17
The second inequality is satisfied, therefore, -2 belongs to the solution set
d. At y = -5:
Inequality 1 .........> -4y + 9 = -4(-5) + 9 = 29 which is not greater than 37
Inequality 2 ........> 3y - 11 = 3(-5) -11 = -26 which is not greater than or equal to 17
Neither of the two inequalities is satisfied, therefore, -5 does not belong to the solution set
e. At y = 6:
Inequality 1 .........> -4y + 9 = -4(6) + 9 = -15 which is not greater than 37
Inequality 2 ........> 3y - 11 = 3(6) - 11 = 7 which is greater than -17
The second inequality is satisfied, therefore, 6 belongs to the solution set
f. At y = -13:
Inequality 1 .........> -4y + 9 = -4(-13) + 9 = 61 which is greater than 37
Inequality 2 ........> 3y - 11 = 3(-13) - 11 = -50 which is not greater than or equal to -17
The first inequality is satisfied, therefore, -13 belongs to the solution set
Hope this helps :)
