Solve the system of equations. y = 15x + 50 y = x^2 + 15x - 50 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. 15x + 50 = x^2 + 15x - 50Subtract to Get Quadratic: Subtract 15x from both sides to get the quadratic equation. 50 = x^2 - 50Add to Isolate x^2: Add 50 to both sides to isolate the x^2 term. 100 = x^2Take Square Root: Take the square root of both sides to solve for x. x = ±10Plug x = 10: Plug x = 10 into one of the original equations to find the corresponding y-value. y = 15(10) + 50 y = 150 + 50 y = 200Plug x = -10: Plug x = -10 into one of the original equations to find the corresponding y-value. y = 15(-10) + 50 y = -150 + 50 y = -100Write Coordinates: Write the coordinates in exact form. First Coordinate: (10, 200) Second Coordinate: (-10, -100)

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Solve the system of equations. $\newline$ $y = 15x + 50$ $\newline$ $y = x^2 + 15x - 50$ $\newline$ 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

Full solution

Q. Solve the system of equations.

\newline

y = 15x + 50

\newline

y = x^2 + 15x - 50

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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 $y$ . $15x + 50 = x^2 + 15x - 50$
Subtract to Get Quadratic: Subtract $15x$ from both sides to get the quadratic equation. $\newline$ $50 = x^2 - 50$
Add to Isolate $x^2$ : Add $50$ to both sides to isolate the $x^2$ term. $\newline$ $100 = x^2$
Take Square Root: Take the square root of both sides to solve for $x$ . $x = \pm 10$
Plug $x = 10$ : Plug $x = 10$ into one of the original equations to find the corresponding $y$ -value. $\newline$ $y = 15(10) + 50$ $\newline$ $y = 150 + 50$ $\newline$ $y = 200$
Plug $x = -10$ : Plug $x = -10$ into one of the original equations to find the corresponding $y$ -value. $\newline$ $y = 15(-10) + 50$ $\newline$ $y = -150 + 50$ $\newline$ $y = -100$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, 200)$ $\newline$ Second Coordinate: $(-10, -100)$