SOLUTION: May someone help me understand this problem. I have looked in my testbook and I can not find an example that can help me solve this problem. The question is: Solve the follo

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Question 6512: May someone help me understand this problem. I have looked in my testbook and I can not find an example that can help me solve this problem.
The question is:
Solve the following sysstem of equations by graphing:
y = x^2 - 4 and y = x - 2.
Thanks,
Angie
Answer by ichudov(499) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28+500%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4%2C+x-2+%29+
the graphs intersect in points where x and y values are the same for both functions. So we can write
x^2-4=x-2
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=2,x=-1.
  • Graphical form: Equation x%5E2-4=x-2 was fully solved.
  • Text form: x^2-4=x-2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%5E2-4=x-2+%29
    For tutors: simplify_cartoon( x^2-4=x-2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%5E2-4=highlight_red%28+x-2+%29.
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+2+%29
It becomes x%5E2-4-highlight_green%28+x+%29%2Bhighlight_green%28+2+%29=0.
Look at x%5E2-highlight_red%28+4+%29-x%2Bhighlight_red%28+2+%29=0.
Added fractions or integers together
It becomes x%5E2%2Bhighlight_green%28+-2+%29-x=0.
Look at x%5E2%2Bhighlight_red%28+-2+%29-x=0.
Moved -2 to the right of expression
It becomes x%5E2-x%2Bhighlight_green%28+-2+%29=0.
Look at x%5E2-x%2Bhighlight_red%28+-2+%29=0.
Removed extra sign in front of -2
It becomes x%5E2-x-highlight_green%28+2+%29=0.
Look at highlight_red%28+x%5E2-x-2+%29=0.
Equation highlight_red%28+x%5E2-x-2=0+%29 is a quadratic equation: x^2-x-2 =0, and has solutions 2,-1
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=2,x=-1.

Universal Simplifier and Solver


Done!