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# Solve the system of equations. Show your work.

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Solve the system of equations. Show your work.

AngelRay  Jun 6, 2018
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$$\boxed{1}\hspace{3mm}y=x^2-3x+4\\ \boxed{2}\hspace{3mm}x+y=4$$

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.
 $$x_1=0$$ $$x-2=0$$ $$x_2=2$$

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. $$0+y=4$$ $$y_1=4$$ $$\boxed{2}\hspace{3mm}x+y=4$$ Substitute for the second option: x=2. $$2+y=4$$ $$y_2=2$$

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

TheXSquaredFactor  Jun 6, 2018