#1**+1 **

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

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. | ||||

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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