Question
Determine whether the ordered pair is a solution of the given system
(-3,-3); 5x + 4y greater then -4
2x + 3y greater then 2
(-3,-3); 5x + 4y greater then -4
2x + 3y greater then 2
Answers
GPT-4o mini
To determine if the ordered pair \((-3, -3)\) is a solution of the given system of inequalities, we will substitute \(x = -3\) and \(y = -3\) into the inequalities and check if they hold true.
1. **First inequality:** \(5x + 4y > -4\)
Substituting \(x = -3\) and \(y = -3\):
\[
5(-3) + 4(-3) > -4
\]
Simplifying the left side:
\[
-15 - 12 > -4
\]
\[
-27 > -4 \quad (\text{This is false.})
\]
2. **Second inequality:** \(2x + 3y > 2\)
Substituting \(x = -3\) and \(y = -3\):
\[
2(-3) + 3(-3) > 2
\]
Simplifying the left side:
\[
-6 - 9 > 2
\]
\[
-15 > 2 \quad (\text{This is also false.})
\]
Since both inequalities do not hold true when substituting the ordered pair \((-3, -3)\), we conclude that the ordered pair \((-3, -3)\) is **not** a solution of the given system of inequalities.
1. **First inequality:** \(5x + 4y > -4\)
Substituting \(x = -3\) and \(y = -3\):
\[
5(-3) + 4(-3) > -4
\]
Simplifying the left side:
\[
-15 - 12 > -4
\]
\[
-27 > -4 \quad (\text{This is false.})
\]
2. **Second inequality:** \(2x + 3y > 2\)
Substituting \(x = -3\) and \(y = -3\):
\[
2(-3) + 3(-3) > 2
\]
Simplifying the left side:
\[
-6 - 9 > 2
\]
\[
-15 > 2 \quad (\text{This is also false.})
\]
Since both inequalities do not hold true when substituting the ordered pair \((-3, -3)\), we conclude that the ordered pair \((-3, -3)\) is **not** a solution of the given system of inequalities.