To determine which ordered pair is a solution to the inequality [tex]\(3x - 4y < 16\)[/tex], we need to evaluate each option by substituting the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] to see if the inequality holds true.
Let's go through each option step-by-step:
### Option a: [tex]\((4, -1)\)[/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ 3(4) - 4(-1) < 16 \][/tex]
[tex]\[ 12 + 4 < 16 \][/tex]
[tex]\[ 16 < 16 \][/tex]
This is false because 16 is not less than 16. Therefore, [tex]\((4, -1)\)[/tex] is not a solution.
### Option b: [tex]\((-3, -3)\)[/tex]
Substitute [tex]\(x = -3\)[/tex] and [tex]\(y = -3\)[/tex] into the inequality:
[tex]\[ 3(-3) - 4(-3) < 16 \][/tex]
[tex]\[ -9 + 12 < 16 \][/tex]
[tex]\[ 3 < 16 \][/tex]
This is true because 3 is indeed less than 16. Therefore, [tex]\((-3, -3)\)[/tex] is a solution.
### Option c: [tex]\((0, -4)\)[/tex]
Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -4\)[/tex] into the inequality:
[tex]\[ 3(0) - 4(-4) < 16 \][/tex]
[tex]\[ 0 + 16 < 16 \][/tex]
[tex]\[ 16 < 16 \][/tex]
This is false because 16 is not less than 16. Therefore, [tex]\((0, -4)\)[/tex] is not a solution.
### Option d: [tex]\((2, -3)\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = -3\)[/tex] into the inequality:
[tex]\[ 3(2) - 4(-3) < 16 \][/tex]
[tex]\[ 6 + 12 < 16 \][/tex]
[tex]\[ 18 < 16 \][/tex]
This is false because 18 is not less than 16. Therefore, [tex]\((2, -3)\)[/tex] is not a solution.
### Conclusion
Only the ordered pair [tex]\((-3, -3)\)[/tex] satisfies the inequality [tex]\(3x - 4y < 16\)[/tex]. Therefore, the correct answer is:
b. [tex]\((-3, -3)\)[/tex]
