Solve the system of equations. y = -26x + 48 y = x^2 - 26x - 33 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 - 26x - 33 becomes -26x + 48 = x^2 - 26x - 33.Simplify Equation: Simplify the equation by adding 26x to both sides and subtracting 48 from both sides: 0 = x^2 - 81.Factor Quadratic Equation: Factor the quadratic equation: 0 = (x - 9)(x + 9).Solve for x: Solve for x by setting each factor equal to zero: x - 9 = 0 or x + 9 = 0.Find x-values: Find the two x-values: x = 9 or x = -9.Substitute x=9: Substitute x = 9 into the first equation to find the corresponding y-value: y = -26(9) + 48.Calculate y for x=9: Calculate the y-value for x = 9: y = -234 + 48.Simplify y for x=9: Simplify to find the y-value: y = -186.Substitute x=-9: Substitute x = -9 into the first equation to find the corresponding y-value: y = -26(-9) + 48.Calculate y for x=-9: Calculate the y-value for x = -9: y = 234 + 48.Simplify y for x=-9: Simplify to find the y-value: y = 282.Write Coordinate Points: Write the solution as coordinate points: (9, -186) and (-9, 282).

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Solve the system of equations. $\newline$ $y = -26x + 48$ $\newline$ $y = x^2 - 26x - 33$ $\newline$ $\newline$ 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.

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y = -26x + 48

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y = x^2 - 26x - 33

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

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(______,______)

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(______,______)

Substitute y Equation: Substitute $y$ from the first equation into the second equation: $y = x^2 - 26x - 33$ becomes $-26x + 48 = x^2 - 26x - 33$ .
Simplify Equation: Simplify the equation by adding $26x$ to both sides and subtracting $48$ from both sides: $0 = x^2 - 81$ .
Factor Quadratic Equation: Factor the quadratic equation: $0 = (x - 9)(x + 9)$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 9 = 0$ or $x + 9 = 0$ .
Find x-values: Find the two x-values: $x = 9$ or $x = -9$ .
Substitute $x=9$ : Substitute $x = 9$ into the first equation to find the corresponding y-value: $y = -26(9) + 48$ .
Calculate $y$ for $x=9$ : Calculate the $y$ -value for $x = 9$ : $y = -234 + 48$ .
Simplify $y$ for $x=9$ : Simplify to find the $y$ -value: $y = -186$ .
Substitute $x=-9$ : Substitute $x = -9$ into the first equation to find the corresponding y-value: $y = -26(-9) + 48$ .
Calculate $y$ for $x=-9$ : Calculate the $y$ -value for $x = -9$ : $y = 234 + 48$ .
Simplify $y$ for $x=-9$ : Simplify to find the $y$ -value: $y = 282$ .
Write Coordinate Points: Write the solution as coordinate points: $(9, -186)$ and $(-9, 282)$ .