Solve the system of equations. y = -32x + 20 y = x^2 - 37x - 16 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 to find x. This gives us -32x + 20 = x^2 - 37x - 16.Rearrange to set to zero: Rearrange the equation to set it to zero: x^2 - 37x + 32x - 16 - 20 = 0. This simplifies to x^2 - 5x - 36 = 0.Factor the quadratic equation: Factor the quadratic equation: (x - 9)(x + 4) = 0.Solve for x: Solve for x by setting each factor equal to zero: x - 9 = 0 or x + 4 = 0. This gives us x = 9 or x = -4.Substitute x=9 into first equation: Substitute x = 9 into the first equation y = -32x + 20 to find y. This gives us y = -32(9) + 20.Calculate y when x=9: Calculate y when x = 9: y = -288 + 20, which simplifies to y = -268.Substitute x=-4 into first equation: Substitute x = -4 into the first equation y = -32x + 20 to find y. This gives us y = -32(-4) + 20.Calculate y when x=-4: Calculate y when x = -4: y = 128 + 20, which simplifies to y = 148.

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Solve the system of equations. $\newline$ $y = -32x + 20$ $\newline$ $y = x^2 - 37x - 16$ $\newline$ 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 = -32x + 20

\newline

y = x^2 - 37x - 16

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into second equation: Substitute $y$ from the first equation into the second equation to find $x$ . This gives us $-32x + 20 = x^2 - 37x - 16$ .
Rearrange to set to zero: Rearrange the equation to set it to zero: $x^2 - 37x + 32x - 16 - 20 = 0$ . This simplifies to $x^2 - 5x - 36 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x - 9)(x + 4) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 9 = 0$ or $x + 4 = 0$ . This gives us $x = 9$ or $x = -4$ .
Substitute $x=9$ into first equation: Substitute $x = 9$ into the first equation $y = -32x + 20$ to find $y$ . This gives us $y = -32(9) + 20$ .
Calculate $y$ when $x=9$ : Calculate $y$ when $x = 9$ : $y = -288 + 20$ , which simplifies to $y = -268$ .
Substitute $x=-4$ into first equation: Substitute $x = -4$ into the first equation $y = -32x + 20$ to find $y$ . This gives us $y = -32(-4) + 20$ .
Calculate $y$ when $x=-4$ : Calculate $y$ when $x = -4$ : $y = 128 + 20$ , which simplifies to $y = 148$ .