Solve the system of equations. y = -35x - 8 y = x^2 - 21x + 5 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. y = -35x - 8 y = x^2 - 21x + 5 So, x^2 - 21x + 5 = -35x - 8.Rearrange and Combine Terms: Rearrange the equation to set it to zero and combine like terms. x^2 - 21x + 5 + 35x + 8 = 0 x^2 + 14x + 13 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 1)(x + 13) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 1 = 0 or x + 13 = 0 This gives us x = -1 or x = -13.Substitute x Values: Substitute x = -1 into one of the original equations to find the corresponding y value. Using y = -35x - 8, we get y = -35(-1) - 8 = 35 - 8 = 27.Write Coordinate Points: Substitute x = -13 into the same original equation to find the corresponding y value. Using y = -35x - 8, we get y = -35(-13) - 8 = 455 - 8 = 447.Write the solution as coordinate points. The coordinate points are (-1, 27) and (-13, 447).

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Solve the system of equations. $\newline$ $y = -35x - 8$ $\newline$ $y = x^2 - 21x + 5$ $\newline$ $\newline$ 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.

\newline

y = -35x - 8

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y = x^2 - 21x + 5

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\newline

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

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(______,______)

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(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = -35x - 8$ $y = x^2 - 21x + 5$ So, $x^2 - 21x + 5 = -35x - 8$ .
Rearrange and Combine Terms: Rearrange the equation to set it to zero and combine like terms. $\newline$ $x^2 - 21x + 5 + 35x + 8 = 0$ $\newline$ $x^2 + 14x + 13 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 1)(x + 13) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 1 = 0$ or $x + 13 = 0$ $\newline$ This gives us $x = -1$ or $x = -13$ .
Substitute $x$ Values: Substitute $x = -1$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = -35x - 8$ , we get $y = -35(-1) - 8 = 35 - 8 = 27$ .
Write Coordinate Points: Substitute $x = -13$ into the same original equation to find the corresponding $y$ value. $\newline$ Using $y = -35x - 8$ , we get $y = -35(-13) - 8 = 455 - 8 = 447$ .
Write Coordinate Points: Substitute $x = -13$ into the same original equation to find the corresponding $y$ value. $\newline$ Using $y = -35x - 8$ , we get $y = -35(-13) - 8 = 455 - 8 = 447$ .Write the solution as coordinate points. $\newline$ The coordinate points are $(-1, 27)$ and $(-13, 447)$ .