Question
3x−4y>12 Which ordered pair (x, y) satisfies the inequality?
Answers
Answered by
GPT-4o mini
To determine which ordered pair \((x, y)\) satisfies the inequality \(3x - 4y > 12\), we can test various pairs in the inequality.
Let's test an example ordered pair: \((6, 0)\).
Substituting \(x = 6\) and \(y = 0\):
\[
3(6) - 4(0) > 12
\]
\[
18 > 12
\]
This is true, so \((6, 0)\) satisfies the inequality.
Now, let’s test another ordered pair: \((2, 0)\).
Substituting \(x = 2\) and \(y = 0\):
\[
3(2) - 4(0) > 12
\]
\[
6 > 12
\]
This is false, so \((2, 0)\) does not satisfy the inequality.
Another example pair to test: \((0, -4)\).
Substituting \(x = 0\) and \(y = -4\):
\[
3(0) - 4(-4) > 12
\]
\[
0 + 16 > 12
\]
\[
16 > 12
\]
This is true, so \((0, -4)\) also satisfies the inequality.
Thus, both \((6, 0)\) and \((0, -4)\) are examples of ordered pairs that satisfy the inequality \(3x - 4y > 12\). You can test more pairs in a similar manner to find additional solutions.
Let's test an example ordered pair: \((6, 0)\).
Substituting \(x = 6\) and \(y = 0\):
\[
3(6) - 4(0) > 12
\]
\[
18 > 12
\]
This is true, so \((6, 0)\) satisfies the inequality.
Now, let’s test another ordered pair: \((2, 0)\).
Substituting \(x = 2\) and \(y = 0\):
\[
3(2) - 4(0) > 12
\]
\[
6 > 12
\]
This is false, so \((2, 0)\) does not satisfy the inequality.
Another example pair to test: \((0, -4)\).
Substituting \(x = 0\) and \(y = -4\):
\[
3(0) - 4(-4) > 12
\]
\[
0 + 16 > 12
\]
\[
16 > 12
\]
This is true, so \((0, -4)\) also satisfies the inequality.
Thus, both \((6, 0)\) and \((0, -4)\) are examples of ordered pairs that satisfy the inequality \(3x - 4y > 12\). You can test more pairs in a similar manner to find additional solutions.