SOLUTION: Hello, I am having a hard time trying to solve this system of eqaution. I hope you can help me. X² - y = -2 X - y = 2 Thank you Fabiana

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: Hello, I am having a hard time trying to solve this system of eqaution. I hope you can help me. X² - y = -2 X - y = 2 Thank you Fabiana      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 181505: Hello,
I am having a hard time trying to solve this system of eqaution. I hope you can help me.
X² - y = -2
X - y = 2
Thank you
Fabiana
Answer by Alan3354(21608) About Me  (Show Source):
You can put this solution on YOUR website!
I am having a hard time trying to solve this system of eqaution. I hope you can help me.
X² - y = -2
X - y = 2
-----------
x - y = 2 --> y = x-2
Sub into the 1st eqn
x%5E2+-%28x-2%29+=+-2
x%5E2+-x+%2B4+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A4=-15.

The discriminant -15 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -15 is + or - sqrt%28+15%29+=+3.87298334620742.

The solution is x%5B12%5D+=+%28--1%2B-i%2Asqrt%28+-15+%29%29%2F2%5C1+=++%28--1%2B-i%2A3.87298334620742%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B4+%29

--------------
Then solve for y, y = x-2