Solve the system of equations. y = 3x + 16 y = x^2 + x - 19 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into second equation: Substitute y from the first equation into the second equation, so we have 3x + 16 = x^2 + x - 19. Rearrange to set to 0: Rearrange the equation to set it to 0: x^2 + x - 19 - 3x - 16 = 0, which simplifies to x^2 - 2x - 35 = 0. Factor the quadratic equation: Factor the quadratic equation: (x - 7)(x + 5) = 0. Solve for x: Solve for x by setting each factor equal to 0: x - 7 = 0 or x + 5 = 0. Find values of x: Find the two values of x: x = 7 and x = -5. Substitute x=7 for y: Substitute x = 7 into the first equation y = 3x + 16 to find the corresponding y value: y = 3(7) + 16. Calculate y for x=7: Calculate y when x = 7: y = 21 + 16, which gives y = 37. Substitute x=-5 for y: Substitute x = -5 into the first equation y = 3x + 16 to find the corresponding y value: y = 3(-5) + 16. Calculate y for x=-5: Calculate y when x = -5: y = -15 + 16, which gives y = 1. Write solutions as coordinate points: Write the solutions as coordinate points: (7, 37) and (-5, 1).

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Solve the system of equations. $\newline$ $y = 3x + 16$ $\newline$ $y = x^2 + x - 19$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,) $\newline$

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Algebra 2

Solve a nonlinear system of equations

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Q. Solve the system of equations.

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y = 3x + 16

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y = x^2 + x - 19

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

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(______,______)

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(______,______)

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Substitute $y$ into second equation: Substitute $y$ from the first equation into the second equation, so we have $3x + 16 = x^2 + x - 19$ .
Rearrange to set to $0$ : Rearrange the equation to set it to $0$ : $x^2 + x - 19 - 3x - 16 = 0$ , which simplifies to $x^2 - 2x - 35 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x - 7)(x + 5) = 0$ .
Solve for x: Solve for x by setting each factor equal to $0$ : $x - 7 = 0$ or $x + 5 = 0$ .
Find values of x: Find the two values of $x$ : $x = 7$ and $x = -5$ .
Substitute $x=7$ for $y$ : Substitute $x = 7$ into the first equation $y = 3x + 16$ to find the corresponding $y$ value: $y = 3(7) + 16$ .
Calculate $y$ for $x=7$ : Calculate $y$ when $x = 7$ : $y = 21 + 16$ , which gives $y = 37$ .
Substitute $x=-5$ for $y$ : Substitute $x = -5$ into the first equation $y = 3x + 16$ to find the corresponding $y$ value: $y = 3(-5) + 16$ .
Calculate $y$ for $x=-5$ : Calculate $y$ when $x = -5$ : $y = -15 + 16$ , which gives $y = 1$ .
Write solutions as coordinate points: Write the solutions as coordinate points: $(7, 37)$ and $(-5, 1)$ .