Question 1051781
.
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:

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-alg-eqns-of-deg2-deg1.lesson>Solving systems of algebraic equations of degree 2 and degree 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-algebraic-equations-of-degree-2.lesson>Solving systems of algebraic equations of degree 2</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Systems-of-equations/Solving-typical-problems-on-systems-of-non-linear-equations-from-the-archive.lesson>Solving typical problems on systems of non-linear equations from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Systems-of-equations/Some-tricks-to-solve-systems-of-non-linear-alg-eqns.lesson>Some tricks to solve systems of non-linear algebraic equations</A> 


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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