Solve the system of equations. y = 39x + 32 y = x^2 + 39x - 17 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Since both equations equal y, set them equal to each other: 39x + 32 = x^2 + 39x - 17.Subtract 39x: Subtract 39x from both sides to get: 32 = x^2 - 17.Add 17: Add 17 to both sides to find x: x^2 = 49.Take Square Root: Take the square root of both sides to solve for x: x = ±7.Plug x = 7: Plug x = 7 into the first equation to find y: y = 39(7) + 32.Calculate y: Calculate y: y = 273 + 32 = 305.Plug x = -7: Now plug x = -7 into the first equation to find y: y = 39(-7) + 32.Calculate y: Calculate y: y = -273 + 32 = -241.

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Solve the system of equations. $\newline$ $y = 39x + 32$ $\newline$ $y = x^2 + 39x - 17$ $\newline$ 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 = 39x + 32

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y = x^2 + 39x - 17

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Since both equations equal $y$ , set them equal to each other: $39x + 32 = x^2 + 39x - 17$ .
Subtract $39x$ : Subtract $39x$ from both sides to get: $32 = x^2 - 17$ .
Add $17$ : Add $17$ to both sides to find $x$ : $x^2 = 49$ .
Take Square Root: Take the square root of both sides to solve for $x$ : $x = \pm 7$ .
Plug $x = 7$ : Plug $x = 7$ into the first equation to find $y$ : $y = 39(7) + 32$ .
Calculate y: Calculate y: $y = 273 + 32 = 305$ .
Plug $x = -7$ : Now plug $x = -7$ into the first equation to find $y$ : $y = 39(-7) + 32$ .
Calculate y: Calculate y: $y = -273 + 32 = -241$ .