Solve the system of equations. y = x^2 + 11x + 42 y = -5x + 3 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. x^2 + 11x + 42 = -5x + 3Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 + 11x + 42 + 5x - 3 = 0 x^2 + 16x + 39 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 3)(x + 13) = 0Solve for x: Set each factor equal to zero and solve for x. x + 3 = 0 or x + 13 = 0 x = -3 or x = -13Substitute x Values: Substitute x = -3 into the second equation to find y. y = -5(-3) + 3 y = 15 + 3 y = 18Find y Values: Substitute x = -13 into the second equation to find y. y = -5(-13) + 3 y = 65 + 3 y = 68Write Coordinates: Write the coordinates in exact form. First Coordinate: (-3, 18) Second Coordinate: (-13, 68)

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Solve the system of equations. $\newline$ $y = x^2 + 11x + 42$ $\newline$ $y = -5x + 3$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a system of linear and quadratic equations: parabolas

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Q. Solve the system of equations.

\newline

y = x^2 + 11x + 42

\newline

y = -5x + 3

\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 $y$ . $x^2 + 11x + 42 = -5x + 3$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 + 11x + 42 + 5x - 3 = 0$ $\newline$ $x^2 + 16x + 39 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 3)(x + 13) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 3 = 0$ or $x + 13 = 0$ $\newline$ $x = -3$ or $x = -13$
Substitute $x$ Values: Substitute $x = -3$ into the second equation to find $y$ . $\newline$ $y = -5(-3) + 3$ $\newline$ $y = 15 + 3$ $\newline$ $y = 18$
Find y Values: Substitute $x = -13$ into the second equation to find $y$ . $y = -5(-13) + 3$ $y = 65 + 3$ $y = 68$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-3, 18)$ $\newline$ Second Coordinate: $(-13, 68)$