The ordered pair that does not belong to the solution set of the inequality 6x+3y(</=)10 is
A. (1, 1)
B. (2, 3)
C. (1, –4)
D. (–3, –3)
To determine the ordered pair that does not belong to the solution set of the inequality 6x + 3y ≤ 10, we can substitute the x and y values of each ordered pair into the inequality and check if the inequality holds true.
Let's go through each option:
A. (1, 1):
Substituting x = 1 and y = 1 into the inequality:
6(1) + 3(1) ≤ 10
6 + 3 ≤ 10
9 ≤ 10
This inequality is true, so (1, 1) belongs to the solution set.
B. (2, 3):
Substituting x = 2 and y = 3 into the inequality:
6(2) + 3(3) ≤ 10
12 + 9 ≤ 10
21 ≤ 10
This inequality is false, so (2, 3) does not belong to the solution set.
C. (1, -4):
Substituting x = 1 and y = -4 into the inequality:
6(1) + 3(-4) ≤ 10
6 - 12 ≤ 10
-6 ≤ 10
This inequality is true, so (1, -4) belongs to the solution set.
D. (-3, -3):
Substituting x = -3 and y = -3 into the inequality:
6(-3) + 3(-3) ≤ 10
-18 - 9 ≤ 10
-27 ≤ 10
This inequality is true, so (-3, -3) belongs to the solution set.
Based on the analysis above, the ordered pair that does not belong to the solution set of the inequality 6x + 3y ≤ 10 is B. (2, 3).
Check each ordered pair.
A.
( 1 , 1 )
x = 1 , y = 1
6 x + 3 y = 6 ∙ 1 + 3 ∙ 1 = 6 + 3 = 9 < 10
belong to the solution
B.
( 2 , 3 )
x = 2 , y = 3
6 x + 3 y = 6 ∙ 2 + 3 ∙ 3 = 12 + 9 = 21 > 10
not belong to the solution
C.
( 1 , - 4 )
x = 1 , y = - 4
6 x + 3 y = 6 ∙ 1 + 3 ∙ ( - 4 ) = 6 - 12 = - 6 < 10
belong to the solution
D.
( - 3 - 3 )
x = - 3 , y = - 3
6 x + 3 y = 6 ∙ ( - 3 ) + 3 ∙ ( - 3 ) = - 18 - 9 = - 27 < 10
belong to the solution
Answer B