Question
From the options below, select the TWO (2) linear inequalities that are shown in this graph of the system.
Red line is dashed and shaded to the left. Blue line is solid and shaded below.
Group of answer choices
x<3
y<3
y>-2x+3
y≤2/3x-2
y≥3
Red line is dashed and shaded to the left. Blue line is solid and shaded below.
Group of answer choices
x<3
y<3
y>-2x+3
y≤2/3x-2
y≥3
Answers
GPT-4o mini
To determine which two linear inequalities correspond to the red dashed line shaded to the left and the blue solid line shaded below, we can analyze each option based on the characteristics of inequalities and shading:
1. **Red line (dashed, shaded to the left)**: This line indicates that the region to the left of the line is included in the solution. Since it's dashed, the line itself is not included (denoted by `<`).
2. **Blue line (solid, shaded below)**: This line indicates that the area below the line is included in the solution. Since it’s solid, the line itself is included (denoted by `≤` or `≥`).
From the choices:
- **x < 3**: This would correspond to a vertical line at x = 3 (not applicable here).
- **y < 3**: This would correspond to a horizontal line at y = 3 (not applicable here).
- **y > -2x + 3**: This would imply shading above the line (not the case here).
- **y ≤ 2/3x - 2**: This indicates a solid line with shading below (could be the blue line).
- **y ≥ 3**: This would correspond to a horizontal line at y = 3 (not applicable here).
Based on the descriptions we analyzed:
1. The red dashed line would be **y < -2x + 3** (inferred as it matches the dashed line behavior).
2. The blue solid line would be **y ≤ 2/3x - 2**.
So, the correct options are:
- **y < -2x + 3** (inferred)
- **y ≤ 2/3x - 2**
(Note: The description of the first inequality should ideally match one of the options provided if any error in deduction exists.)
1. **Red line (dashed, shaded to the left)**: This line indicates that the region to the left of the line is included in the solution. Since it's dashed, the line itself is not included (denoted by `<`).
2. **Blue line (solid, shaded below)**: This line indicates that the area below the line is included in the solution. Since it’s solid, the line itself is included (denoted by `≤` or `≥`).
From the choices:
- **x < 3**: This would correspond to a vertical line at x = 3 (not applicable here).
- **y < 3**: This would correspond to a horizontal line at y = 3 (not applicable here).
- **y > -2x + 3**: This would imply shading above the line (not the case here).
- **y ≤ 2/3x - 2**: This indicates a solid line with shading below (could be the blue line).
- **y ≥ 3**: This would correspond to a horizontal line at y = 3 (not applicable here).
Based on the descriptions we analyzed:
1. The red dashed line would be **y < -2x + 3** (inferred as it matches the dashed line behavior).
2. The blue solid line would be **y ≤ 2/3x - 2**.
So, the correct options are:
- **y < -2x + 3** (inferred)
- **y ≤ 2/3x - 2**
(Note: The description of the first inequality should ideally match one of the options provided if any error in deduction exists.)