How can you use a website to visualize the solutions to a system of equations?

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SUMMARY

The discussion focuses on visualizing the solutions to the system of equations y=x^2 - x - 8 and y=2x+10. The intersection points of these equations are identified as (1, 2) and (28, 34). Users can utilize the online tool available at http://www.softintegration.com/chhtml/lang/lib/libch/plot/cgi_func.html to plot the equations and visually confirm the solutions. The method involves setting the equations equal to each other to solve for x and then substituting back to find corresponding y values.

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  • Understanding of quadratic equations and linear equations
  • Familiarity with graphing functions
  • Basic knowledge of intersection points in coordinate geometry
  • Experience using online graphing tools
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  • Learn how to use the online graphing tool at http://www.softintegration.com/chhtml/lang/lib/libch/plot/cgi_func.html
  • Study the methods for solving systems of equations algebraically
  • Explore the concept of function intersections in calculus
  • Investigate the implications of quadratic and linear function behaviors
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Students, educators, and anyone interested in mathematics, particularly those focusing on algebra and graphing techniques for solving systems of equations.

meatandpotatoes22003
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the system is:

y=x^2 - x - 8
y=2x+10

the answer is: 1 and 28

Can someone break this down how they arrived at these figures?

thank you.
 
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Set them equal to each other to solve for x, then plug the corresponding y values into find 2x + y.
 
Or you can go to http://www.softintegration.com/chhtml/lang/lib/libch/plot/cgi_func.html

go down the page and put into "Number of Data Sets to Plot : 2", because you have two equations.

Then you click submit, and in next page you enter your functions:

Curve #1
y= pow(x,2) -x -8

Curve #2
y=2*x+10

Now as you can see your two graphs intersect each other at the point of your x and y solutions. There are 2 points that satisfy this system of equations.

And as for answer (Find 2x+y) there are 2 answers to that question: 34 and 2
 
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