Solve the system of equations. y = 5x^2 + 2x - 1 y = -8x - 6 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. 5x^2 + 2x - 1 = -8x - 6Move Terms to Form Quadratic: Move all terms to one side to form a quadratic equation. 5x^2 + 2x - 1 + 8x + 6 = 0 5x^2 + 10x + 5 = 0Factor Quadratic Equation: Factor the quadratic equation if possible. The quadratic equation 5x^2 + 10x + 5 can be factored as (5x + 5)(x + 1).Solve for x: Solve for x by setting each factor equal to zero. (5x + 5) = 0 and (x + 1) = 0 Solving these gives x = -1 and x = -1. We only have one unique solution for x.Substitute x to Find y: Substitute x back into one of the original equations to find the corresponding y value. Using y = -8x - 6 and substituting x = -1 gives y = -8(-1) - 6 = 8 - 6 = 2.Write Coordinates: Write the coordinates in exact form. The coordinates of the intersection point are (-1, 2).

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Solve the system of equations. $\newline$ $y = 5x^2 + 2x - 1$ $\newline$ $y = -8x - 6$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,)

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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 = 5x^2 + 2x - 1

\newline

y = -8x - 6

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

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $5x^2 + 2x - 1 = -8x - 6$
Move Terms to Form Quadratic: Move all terms to one side to form a quadratic equation. $\newline$ $5x^2 + 2x - 1 + 8x + 6 = 0$ $\newline$ $5x^2 + 10x + 5 = 0$
Factor Quadratic Equation: Factor the quadratic equation if possible. $\newline$ The quadratic equation $5x^2 + 10x + 5$ can be factored as $(5x + 5)(x + 1)$ .
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(5x + 5) = 0$ and $(x + 1) = 0$ $\newline$ Solving these gives $x = -1$ and $x = -1$ . We only have one unique solution for $x$ .
Substitute $x$ to Find $y$ : Substitute $x$ back into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = -8x - 6$ and substituting $x = -1$ gives $y = -8(-1) - 6 = 8 - 6 = 2$ .
Write Coordinates: Write the coordinates in exact form. $\newline$ The coordinates of the intersection point are $(-1, 2)$ .