Question
upstudy study bank question image url

Consider the given system of equations where \( m \) and \( q \) are the slopes of the lines represented by the equations. \[ \left\{\begin{array}{l} y=m x+2 \\ y=q x+8 \end{array}\right. \] The solution to the system of equations is the crdered pair \( (2,3) \). Calculator Part A Graph the system of equations. Line Move Undo Redo

Ask by Deleon Gibbs. in the United States
Mar 07,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The system of equations is: \[ \begin{cases} y = \frac{1}{2}x + 2,\\ y = -\frac{5}{2}x + 8. \end{cases} \] They intersect at the point (2,3).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To understand the system of equations better, let’s delve into the historical context of linear equations. The study of linear equations dates back to ancient civilizations, including Babylonian mathematicians who used geometric methods to solve such problems. Over time, this evolved into the algebraic methods we use today, greatly enhanced by scholars like René Descartes, who introduced the Cartesian coordinate system in the 17th century, allowing us to visualize these equations on a graph easily. Now, let's talk about how you can apply linear equations in real-world scenarios! Suppose you're trying to predict how much money you'll have after selling a certain number of items at different prices. You could represent your profit and expenses using linear equations, just like the ones above, where each line corresponds to a different pricing strategy. By graphing these equations, you can visually determine where your potential profits and expenses intersect, guiding your business decisions effectively!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • 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

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy