Solve the system of equations. y = -x + 21 y = x^2 - 9x + 36 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. y = -x + 21 y = x^2 - 9x + 36 So, -x + 21 = x^2 - 9x + 36Rearrange and Solve: Rearrange the equation to set it to zero and solve for x. 0 = x^2 - 9x + 36 + x - 21 0 = x^2 - 8x + 15Factor Quadratic Equation: Factor the quadratic equation. 0 = (x - 3)(x - 5)Solve for x: Solve for x by setting each factor equal to zero. x - 3 = 0 or x - 5 = 0 So, x = 3 or x = 5Substitute x Values: Substitute x = 3 into one of the original equations to find the corresponding y value. Using y = -x + 21, we get y = -(3) + 21 = 18Find Corresponding y Values: Substitute x = 5 into one of the original equations to find the corresponding y value. Using y = -x + 21, we get y = -(5) + 21 = 16Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (3, 18) and (5, 16).

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Solve the system of equations. $\newline$ $y = -x + 21$ $\newline$ $y = x^2 - 9x + 36$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a nonlinear system of equations

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Q. Solve the system of equations.

\newline

y = -x + 21

\newline

y = x^2 - 9x + 36

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = -x + 21$ $y = x^2 - 9x + 36$ So, $-x + 21 = x^2 - 9x + 36$
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ . $0 = x^2 - 9x + 36 + x - 21$ $0 = x^2 - 8x + 15$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $0 = (x - 3)(x - 5)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 3 = 0$ or $x - 5 = 0$ $\newline$ So, $x = 3$ or $x = 5$
Substitute $x$ Values: Substitute $x = 3$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = -x + 21$ , we get $y = -(3) + 21 = 18$
Find Corresponding y Values: Substitute $x = 5$ into one of the original equations to find the corresponding y value. $\newline$ Using $y = -x + 21$ , we get $y = -(5) + 21 = 16$
Write Coordinate Points: Write the solution as coordinate points. $\newline$ The coordinate points are $(3, 18)$ and $(5, 16)$ .