Question
Which point would be a solution to the system of linear inequalities
shown below?
\[ y-\frac{2}{3} x-7 \]
Answer
\( \begin{array}{l}(-6,-7) \\ (-6,10) \\ (3,0) \\ (-9,0)\end{array} \)
Ask by Donnelly Gibson. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The point (3, 0) is the solution to the system of inequalities.
Solution
To solve the system, we substitute each point into the inequalities and check:
System:
(1) y < x + 1
(2) y > (-2/3)x – 7
Check each candidate:
1. For (–6, –7):
Inequality (1): –7 < (–6 + 1) → –7 < –5 (true)
Inequality (2): –7 > (–2/3)(–6) – 7 = 4 – 7 = –3 → –7 > –3 (false)
2. For (–6, 10):
Inequality (1): 10 < (–6 + 1) → 10 < –5 (false)
3. For (3, 0):
Inequality (1): 0 < (3 + 1) → 0 < 4 (true)
Inequality (2): 0 > (–2/3)(3) – 7 = –2 – 7 = –9 → 0 > –9 (true)
4. For (–9, 0):
Inequality (1): 0 < (–9 + 1) → 0 < –8 (false)
Only point (3, 0) satisfies both inequalities.
Thus, the solution is (3, 0).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To determine which point satisfies the system of inequalities, we can substitute the coordinates of each point into the inequalities. For instance, the point \((-6,10)\) leads to \(10 < -6 + 1\) (which is false) and \(10 > -\frac{2}{3}(-6) - 7\) (which is true). So this point isn’t the solution. Now, let’s check the final point \((-9,0)\). For this point, we find \(0 < -9 + 1\) (which is false) and \(0 > -\frac{2}{3}(-9) - 7\) (which is true). Testing each point diligently will lead to the right solution!
