Solve the system of equations. Show your work.

 Jun 6, 2018

\(\boxed{1}\hspace{3mm}y=x^2-3x+4\\ \boxed{2}\hspace{3mm}x+y=4\)


In the system of equations, the first equation is already solver for, so I can substitute its value into the second question. 


\(y=\textcolor{red}{x^2-3x+4};\\ x+\textcolor{red}{y}=4\) Use substitution to get rid of one variable. 
\(x+\textcolor{red}{x^2-3x+4}=4\) Combine like terms and subtract 4 from both sides. 
\(x^2-2x=0\) Factor the GCF of the left-hand side of the equation: x. 
\(x(x-2)=0\) Set both factors equal to 0 and solve. 
\(x_1=0\) \(x-2=0\)




Let's substitute both possibilities for y: 


\(\boxed{2}\hspace{3mm}x+y=4\) Let's substitute in the first possibility for x: x=0.
\(\boxed{2}\hspace{3mm}x+y=4\) Substitute for the second option: x=2.


Here are the answers in coordinate form: \((0,4)\) and \((2,2)\)

 Jun 6, 2018

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