Hamilton Williams
04/07/2024 · Senior High School

Solve the system of linear inequalities by graphing. \( \begin{array}{l}2 x+y>8 \\ 2 x+y<-1\end{array} \)

UpStudy ThothAI Solution

Tutor-Verified Answer

Step-by-step Solution

I will solve the system of linear inequalities by graphing them on a coordinate plane. The system of linear inequalities is: \[ \begin{array}{l} 2x + y > 8 \\ 2x + y < -1 \end{array} \] To solve this system by graphing, we will graph the two lines \(2x + y = 8\) and \(2x + y = -1\) and then determine the region that satisfies both inequalities. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+y=8\\2x+y=-1\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=8-2x\\2x+y=-1\end{array}\right.\) - step2: Substitute the value of \(y:\) \(2x+8-2x=-1\) - step3: Remove the opposites: \(8=-1\) - step4: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\) - step5: Rewrite: \((x, y) \in \varnothing\) The system of linear inequalities \(2x + y > 8\) and \(2x + y < -1\) has no solution. This means that there is no region on the coordinate plane that satisfies both inequalities simultaneously.

Quick Answer

The system of linear inequalities \(2x + y > 8\) and \(2x + y < -1\) has no solution.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text

Enter your question here…

By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
📸 STUDY CAN BE A REAL STRUGGLE
Why Not UpStudy It?
Select your plan below
Premium

You can enjoy

  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to answer and
    solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic
  • Limited Solutions