SOLUTION: x^2+y^2=1 x+y=-1 can you give me the steps to solve this problem using simple words because i do not understand the steps they show me in my book

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Question 217702: x^2+y^2=1
x+y=-1
can you give me the steps to solve this problem using simple words because i do not understand the steps they show me in my book
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=1 This is an equation of a circle centered at point (0,0) with radius 1.

x%2By=-1 This is an equation of a line with slope m=-1 and y-intercept at b=-1 or at point (0,-1).

Step 1. Let's solve for x in x%2By=-1

Subtract -y to both sides of the equation

x%2By-y=-1-y=-1%281%2By%29=-1%28y%2B1%29}

x=-1%28y%2B1%29

Step 2. Substitute x=-1%28y%2B1%29 into x%5E2%2By%5E2=1

x%5E2%2By%5E2=1=+%28-1%29%5E2%28y%2B1%29%5E2%2By%5E2 but %28-1%29%5E2=1 and %28y%2B1%29%5E2=y%5E2%2B2y%2B1

x%5E2%2By%5E2=y%5E2%2B2y%2B1%2By%5E2=1

2y%5E2%2B2y%2B1=1

Step 3. Subtract 1 to both sides of the equation

2y%5E2%2B2y%2B1-1=1-1

2y%5E2%2B2y=0

2y%28y%2B1%29=0

Then y=0 and y=-1

Step 4. Find x-coordinates when y=0 and y=-1

At y=0, then x=-1-y=-1-0=-1. One intersection point is (-1,0).

At y=-1 then x=-1-%28-1%29=-1%2B1=0. One intersection point is (0,-1).

Step 5. Then intersection points are (-1,0) and (0,-1)

Here are the graphs of the circle and line and note they have two common points.






I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J