Question
etermine if the point (3,8) is a solution to the simultaneous inequalities y>x+5 and y≤6x−3
. Select the response that gives the correct answer as well as the correct reasoning.(1 point)
Responses
Yes, because both of these inequalities include points on the line as a solution
Yes, because both of these inequalities include points on the line as a solution
Yes, it is within the solution set for both inequalities
Yes, it is within the solution set for both inequalities
No, it is not in the solution set for either inequality.
No, it is not in the solution set for either inequality.
No, it is in the solution set for y<6x−3
, but not for y>x+5
No, it is in the solution set for y<6x−3
, but not for y is greater than x plus 5
. Select the response that gives the correct answer as well as the correct reasoning.(1 point)
Responses
Yes, because both of these inequalities include points on the line as a solution
Yes, because both of these inequalities include points on the line as a solution
Yes, it is within the solution set for both inequalities
Yes, it is within the solution set for both inequalities
No, it is not in the solution set for either inequality.
No, it is not in the solution set for either inequality.
No, it is in the solution set for y<6x−3
, but not for y>x+5
No, it is in the solution set for y<6x−3
, but not for y is greater than x plus 5
Answers
GPT-4o mini
To determine if the point (3, 8) is a solution to the inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we need to test the point against both inequalities.
1. For the inequality \( y > x + 5 \):
- Substitute \( x = 3 \) and \( y = 8 \):
- \( 8 > 3 + 5 \)
- \( 8 > 8 \) which is **not true**.
- So, (3, 8) does not satisfy this inequality.
2. For the inequality \( y \leq 6x - 3 \):
- Substitute \( x = 3 \) and \( y = 8 \):
- \( 8 \leq 6(3) - 3 \)
- \( 8 \leq 18 - 3 \)
- \( 8 \leq 15 \) which is **true**.
- So, (3, 8) satisfies this inequality.
Based on this analysis, we conclude that the point (3, 8) is **not a solution** to the first inequality but is a solution to the second inequality.
The correct response is:
**No, it is in the solution set for \( y \leq 6x - 3 \), but not for \( y > x + 5 \).**
1. For the inequality \( y > x + 5 \):
- Substitute \( x = 3 \) and \( y = 8 \):
- \( 8 > 3 + 5 \)
- \( 8 > 8 \) which is **not true**.
- So, (3, 8) does not satisfy this inequality.
2. For the inequality \( y \leq 6x - 3 \):
- Substitute \( x = 3 \) and \( y = 8 \):
- \( 8 \leq 6(3) - 3 \)
- \( 8 \leq 18 - 3 \)
- \( 8 \leq 15 \) which is **true**.
- So, (3, 8) satisfies this inequality.
Based on this analysis, we conclude that the point (3, 8) is **not a solution** to the first inequality but is a solution to the second inequality.
The correct response is:
**No, it is in the solution set for \( y \leq 6x - 3 \), but not for \( y > x + 5 \).**