SOLUTION: y=-x^2+4x-3 y=x-2

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Question 1051781: y=-x^2+4x-3
y=x-2
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x-2=-x%5E2%2B4x-3
x%5E2-3x%2B1=0
x%5E2-3x%2B%283%2F2%29%5E2%2B1=%283%2F2%29%5E2
%28x-3%2F2%29%5E2=%283%2F2%29%5E2-1
%28x-3%2F2%29%5E2=9%2F4-4%2F4
%28x-3%2F2%29%5E2=5%2F4
x-3%2F2=0+%2B-+sqrt%285%29%2F2
x=3%2F2+%2B-+sqrt%285%29%2F2
x=%283%2B-sqrt%285%29%29%2F2
and correspondingly,
y=%28-1%2B-+sqrt%285%29%29%2F2
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Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
y = -x^2+4x-3
y = x-2
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Since the left sides are identical, then the right sides are equal:
x - 2 = -x^2 + 4x -3.

Since you just work on systems of non-linear equation, you, probably can easily solve this quadratic equation.


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There are lessons in this site related to solving systems of non-linear equations.
They might be of interest for you:
    - Solving systems of algebraic equations of degree 2 and degree 1
    - Solving systems of algebraic equations of degree 2

    - Solving typical problems on systems of non-linear equations from the archive
    - Some tricks to solve systems of non-linear algebraic equations

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of equations that are not linear".