Question
Which of the following points is a solution to the linear inequality 4x−y≤104x−y≤10 as shown on the graph? (1 point) Responses (5, 0)(5, 0)(5, 0)(5, 0) (3.5, −1)(3.5, −1)(3.5, −1)(3.5, −1) (2,−2)(2,−2)open paren 2 comma negative 2 close paren (3, 0)
Answers
Answered by
GPT-4o mini
To determine which of the given points is a solution to the inequality \(4x - y \leq 10\), we will evaluate each point:
1. **For the point (5, 0)**:
\[
4(5) - 0 = 20 \quad \text{which is not less than or equal to } 10.
\]
So, (5, 0) is **not** a solution.
2. **For the point (3.5, -1)**:
\[
4(3.5) - (-1) = 14 + 1 = 15 \quad \text{which is not less than or equal to } 10.
\]
So, (3.5, -1) is **not** a solution.
3. **For the point (2, -2)**:
\[
4(2) - (-2) = 8 + 2 = 10 \quad \text{which is equal to } 10.
\]
So, (2, -2) **is** a solution.
4. **For the point (3, 0)**:
\[
4(3) - 0 = 12 \quad \text{which is not less than or equal to } 10.
\]
So, (3, 0) is **not** a solution.
The only point that satisfies the inequality \(4x - y \leq 10\) is **(2, -2)**.
1. **For the point (5, 0)**:
\[
4(5) - 0 = 20 \quad \text{which is not less than or equal to } 10.
\]
So, (5, 0) is **not** a solution.
2. **For the point (3.5, -1)**:
\[
4(3.5) - (-1) = 14 + 1 = 15 \quad \text{which is not less than or equal to } 10.
\]
So, (3.5, -1) is **not** a solution.
3. **For the point (2, -2)**:
\[
4(2) - (-2) = 8 + 2 = 10 \quad \text{which is equal to } 10.
\]
So, (2, -2) **is** a solution.
4. **For the point (3, 0)**:
\[
4(3) - 0 = 12 \quad \text{which is not less than or equal to } 10.
\]
So, (3, 0) is **not** a solution.
The only point that satisfies the inequality \(4x - y \leq 10\) is **(2, -2)**.