Solve the system of equations. y = 49x + 33 y = x^2 + 36x - 15 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation: x^2 + 36x - 15 = 49x + 33.Rearrange and Set to 0: Rearrange the equation to set it to 0: x^2 + 36x - 49x - 15 - 33 = 0.Simplify Equation: Simplify the equation: x^2 - 13x - 48 = 0.Factor Quadratic Equation: Factor the quadratic equation: (x - 16)(x + 3) = 0.Solve for x: Solve for x: x = 16 or x = -3.Find y for x=16: Substitute x = 16 into the first equation to find y: y = 49(16) + 33.Calculate y for x=16: Calculate y when x = 16: y = 784 + 33.Find y for x=-3: Simplify to find y: y = 817.Calculate y for x=-3: Substitute x = -3 into the first equation to find y: y = 49(-3) + 33.Calculate y when x = -3: y = -147 + 33.Simplify to find y: y = -114.

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Solve the system of equations. $\newline$ $y = 49x + 33$ $\newline$ $y = x^2 + 36x - 15$ $\newline$ 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 = 49x + 33

\newline

y = x^2 + 36x - 15

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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: $x^2 + 36x - 15 = 49x + 33$ .
Rearrange and Set to $0$ : Rearrange the equation to set it to $0$ : $x^2 + 36x - 49x - 15 - 33 = 0$ .
Simplify Equation: Simplify the equation: $x^2 - 13x - 48 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation: $(x - 16)(x + 3) = 0$ .
Solve for x: Solve for x: $x = 16$ or $x = -3$ .
Find $y$ for $x=16$ : Substitute $x = 16$ into the first equation to find $y$ : $y = 49(16) + 33$ .
Calculate $y$ for $x=16$ : Calculate $y$ when $x = 16$ : $y = 784 + 33$ .
Find $y$ for $x=-3$ : Simplify to find $y$ : $y = 817$ .
Calculate $y$ for $x=-3$ : Substitute $x = -3$ into the first equation to find $y$ : $y = 49(-3) + 33$ .
Calculate $y$ for $x=-3$ : Substitute $x = -3$ into the first equation to find $y$ : $y = 49(-3) + 33$ .Calculate $y$ when $x = -3$ : $y = -147 + 33$ .
Calculate $y$ for $x=-3$ : Substitute $x = -3$ into the first equation to find $y$ : $y = 49(-3) + 33$ .Calculate $y$ when $x = -3$ : $y = -147 + 33$ .Simplify to find $y$ : $y = -114$ .