Question
A system of inequalities is shown:
Inequality 1: x≤5
Inequality 2: y>−2x+3
Which statement is true for the point (0, 3) ?
(1 point)
Responses
The point (0,3) is a solution for inequality 2 but not inequality 1.
The point open paren 0 comma 3 close paren is a solution for inequality 2 but not inequality 1.
The point (0, 3) is not a solution for this system of linear inequalities.
The point (0, 3) is not a solution for this system of linear inequalities.
The point (0, 3) is one of many solutions for this system of linear inequalities.
The point (0, 3) is one of many solutions for this system of linear inequalities.
The point (0, 3) is the only solution for this system of linear inequalities.
Inequality 1: x≤5
Inequality 2: y>−2x+3
Which statement is true for the point (0, 3) ?
(1 point)
Responses
The point (0,3) is a solution for inequality 2 but not inequality 1.
The point open paren 0 comma 3 close paren is a solution for inequality 2 but not inequality 1.
The point (0, 3) is not a solution for this system of linear inequalities.
The point (0, 3) is not a solution for this system of linear inequalities.
The point (0, 3) is one of many solutions for this system of linear inequalities.
The point (0, 3) is one of many solutions for this system of linear inequalities.
The point (0, 3) is the only solution for this system of linear inequalities.
Answers
GPT-4o mini
To determine which statement is true for the point (0, 3) based on the given system of inequalities, we will evaluate each inequality:
1. **Inequality 1: \(x \leq 5\)**
- For the point (0, 3), we have \(x = 0\).
- Since \(0 \leq 5\) is true, the point (0, 3) satisfies Inequality 1.
2. **Inequality 2: \(y > -2x + 3\)**
- For the point (0, 3), we have \(y = 3\) and \(x = 0\).
- Substitute \(x = 0\) into the inequality:
\[
y > -2(0) + 3 \implies y > 3
\]
- Since \(3 > 3\) is false, the point (0, 3) does not satisfy Inequality 2.
Now we can summarize the results:
- The point (0, 3) satisfies Inequality 1.
- The point (0, 3) does not satisfy Inequality 2.
Based on the evaluations, the correct statement is:
**The point (0, 3) is a solution for inequality 1 but not inequality 2.**
None of the provided options perfectly match this statement; however, based on the evaluations, the point is a solution for one inequality and not the other. Thus, the most applicable conclusion is:
**The point (0, 3) is not a solution for this system of linear inequalities.**
This is because for a point to be a solution to a system of inequalities, it must satisfy all inequalities in the system. Since it does not satisfy Inequality 2, it is indeed not a solution for the system.
1. **Inequality 1: \(x \leq 5\)**
- For the point (0, 3), we have \(x = 0\).
- Since \(0 \leq 5\) is true, the point (0, 3) satisfies Inequality 1.
2. **Inequality 2: \(y > -2x + 3\)**
- For the point (0, 3), we have \(y = 3\) and \(x = 0\).
- Substitute \(x = 0\) into the inequality:
\[
y > -2(0) + 3 \implies y > 3
\]
- Since \(3 > 3\) is false, the point (0, 3) does not satisfy Inequality 2.
Now we can summarize the results:
- The point (0, 3) satisfies Inequality 1.
- The point (0, 3) does not satisfy Inequality 2.
Based on the evaluations, the correct statement is:
**The point (0, 3) is a solution for inequality 1 but not inequality 2.**
None of the provided options perfectly match this statement; however, based on the evaluations, the point is a solution for one inequality and not the other. Thus, the most applicable conclusion is:
**The point (0, 3) is not a solution for this system of linear inequalities.**
This is because for a point to be a solution to a system of inequalities, it must satisfy all inequalities in the system. Since it does not satisfy Inequality 2, it is indeed not a solution for the system.