Solve the system of equations. y = x^2 + 44x + 8 y = 44x + 44 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^2 + 44x + 8 y = 44x + 44 So, x^2 + 44x + 8 = 44x + 44Subtract and Simplify: Subtract 44x + 44 from both sides to set the equation to zero. x^2 + 44x + 8 - (44x + 44) = 0 This simplifies to x^2 - 36 = 0Factor Quadratic Equation: Factor the quadratic equation. x^2 - 36 = (x + 6)(x - 6) = 0Solve for x: Solve for x using the zero product property. x + 6 = 0 or x - 6 = 0 This gives us x = -6 or x = 6Substitute x = -6: Substitute x = -6 into one of the original equations to find the corresponding y value. Using y = 44x + 44, we get y = 44(-6) + 44 = -264 + 44 = -220 So one point of intersection is (-6, -220).Substitute x = 6: Substitute x = 6 into one of the original equations to find the corresponding y value. Using y = 44x + 44, we get y = 44(6) + 44 = 264 + 44 = 308 So the other point of intersection is (6, 308).

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Solve the system of equations. $\newline$ $y = x^2 + 44x + 8$ $\newline$ $y = 44x + 44$ $\newline$ 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^2 + 44x + 8

\newline

y = 44x + 44

\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 $y$ . $y = x^2 + 44x + 8$ $y = 44x + 44$ So, $x^2 + 44x + 8 = 44x + 44$
Subtract and Simplify: Subtract $44x + 44$ from both sides to set the equation to zero. $\newline$ $x^2 + 44x + 8 - (44x + 44) = 0$ $\newline$ This simplifies to $x^2 - 36 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $x^2 - 36 = (x + 6)(x - 6) = 0$
Solve for x: Solve for x using the zero product property. $\newline$ $x + 6 = 0$ or $x - 6 = 0$ $\newline$ This gives us $x = -6$ or $x = 6$
Substitute $x = -6$ : Substitute $x = -6$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 44x + 44$ , we get $y = 44(-6) + 44 = -264 + 44 = -220$ $\newline$ So one point of intersection is $(-6, -220)$ .
Substitute $x = 6$ : Substitute $x = 6$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 44x + 44$ , we get $y = 44(6) + 44 = 264 + 44 = 308$ $\newline$ So the other point of intersection is $(6, 308)$ .