Solve the system of equations. y = 2x^2 - 15x - 16 y = -15x + 2 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = 2x^2 - 15x - 16 y = -15x + 2 Set the two equations equal to each other to find the x-values where they intersect. 2x^2 - 15x - 16 = -15x + 2Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 2x^2 - 15x - 16 + 15x - 2 = 0 2x^2 - 18 = 0Isolate Quadratic Term: Add 18 to both sides to isolate the quadratic term. 2x^2 = 18Solve for x: Divide both sides by 2 to solve for x^2. x^2 = 9Substitute x into Equation: Take the square root of both sides to solve for x. x = ±3Calculate y Values: Find the corresponding y-values for each x-value by substituting x into one of the original equations. Let's use y = -15x + 2. For x = 3: y = -15(3) + 2 y = -45 + 2 y = -43Write Coordinates: For x = -3: y = -15(-3) + 2 y = 45 + 2 y = 47Write the coordinates in exact form. First Coordinate: (3, -43) Second Coordinate: (-3, 47)

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Solve the system of equations. $\newline$ $y = 2x^2 - 15x - 16$ $\newline$ $y = -15x + 2$ $\newline$ 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 = 2x^2 - 15x - 16

\newline

y = -15x + 2

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = 2x^2 - 15x - 16$ $\newline$ $y = -15x + 2$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $2x^2 - 15x - 16 = -15x + 2$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $2x^2 - 15x - 16 + 15x - 2 = 0$ $\newline$ $2x^2 - 18 = 0$
Isolate Quadratic Term: Add $18$ to both sides to isolate the quadratic term. $\newline$ $2x^2 = 18$
Solve for x: Divide both sides by $2$ to solve for $x^2$ . $x^2 = 9$
Substitute $x$ into Equation: Take the square root of both sides to solve for $x$ . $x = \pm 3$
Calculate y Values: Find the corresponding $y$ -values for each $x$ -value by substituting $x$ into one of the original equations. Let's use $y = -15x + 2$ . For $x = 3$ : $y = -15(3) + 2$ $y = -45 + 2$ $y = -43$
Write Coordinates: For $x = -3$ : $\newline$ $y = -15(-3) + 2$ $\newline$ $y = 45 + 2$ $\newline$ $y = 47$
Write Coordinates: For $x = -3$ : $y = -15(-3) + 2$ $y = 45 + 2$ $y = 47$ Write the coordinates in exact form. $\text{First Coordinate: } (3, -43)$ $\text{Second Coordinate: } (-3, 47)$