Solve the system of equations. y = 3x - 44 y = x^2 - 15x - 12 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation: y = x^2 - 15x - 12 becomes 3x - 44 = x^2 - 15x - 12.Rearrange to Set to 0: Rearrange the equation to set it to 0: x^2 - 15x - 12 - 3x + 44 = 0, which simplifies to x^2 - 18x + 32 = 0.Factor Quadratic Equation: Factor the quadratic equation: (x - 16)(x - 2) = 0.Solve for x: Solve for x: x = 16 or x = 2.Substitute x = 16: Substitute x = 16 into the first equation to find y: y = 3(16) - 44, y = 48 - 44, y = 4.Substitute x = 2: Substitute x = 2 into the first equation to find y: y = 3(2) - 44, y = 6 - 44, y = -38.

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Solve the system of equations. $\newline$ $y = 3x - 44$ $\newline$ $y = x^2 - 15x - 12$ $\newline$ 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 = 3x - 44

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y = x^2 - 15x - 12

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

\newline

(______,______)

\newline

(______,______)

Substitute y Equation: Substitute $y$ from the first equation into the second equation: $y = x^2 - 15x - 12$ becomes $3x - 44 = x^2 - 15x - 12$ .
Rearrange to Set to $0$ : Rearrange the equation to set it to $0$ : $x^2 - 15x - 12 - 3x + 44 = 0$ , which simplifies to $x^2 - 18x + 32 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation: $(x - 16)(x - 2) = 0$ .
Solve for x: Solve for x: $x = 16$ or $x = 2$ .
Substitute $x = 16$ : Substitute $x = 16$ into the first equation to find $y$ : $y = 3(16) - 44$ , $y = 48 - 44$ , $y = 4$ .
Substitute $x = 2$ : Substitute $x = 2$ into the first equation to find $y$ : $y = 3(2) - 44$ , $y = 6 - 44$ , $y = -38$ .