Solve the system of equations. y = -21x - 14 y = x^2 - 4x + 28 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: y = x^2 - 4x + 28 becomes -21x - 14 = x^2 - 4x + 28.Rearrange to set to 0: Rearrange the equation to set it to 0: x^2 - 4x + 28 + 21x + 14 = 0, which simplifies to x^2 + 17x + 42 = 0.Factor the quadratic equation: Factor the quadratic equation: (x + 7)(x + 6) = 0.Solve for x: Solve for x by setting each factor equal to 0: x + 7 = 0 or x + 6 = 0.Find first x value: Find the first value of x: x = -7.Find second x value: Find the second value of x: x = -6.Substitute x=-7 for y: Substitute x = -7 into the first equation to find y: y = -21(-7) - 14.Calculate y for x=-7: Calculate y for x = -7: y = 147 - 14, which simplifies to y = 133.Substitute x=-6 for y: Substitute x = -6 into the first equation to find y: y = -21(-6) - 14.Calculate y for x=-6: Calculate y for x = -6: y = 126 - 14, which simplifies to y = 112.Write solution as coordinate points: Write the solution as coordinate points: (-7, 133) and (-6, 112).

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Solve the system of equations. $\newline$ $y = -21x - 14$ $\newline$ $y = x^2 - 4x + 28$ $\newline$ 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 = -21x - 14

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y = x^2 - 4x + 28

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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: $y = x^2 - 4x + 28$ becomes $-21x - 14 = x^2 - 4x + 28$ .
Rearrange to set to $0$ : Rearrange the equation to set it to $0$ : $x^2 - 4x + 28 + 21x + 14 = 0$ , which simplifies to $x^2 + 17x + 42 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x + 7)(x + 6) = 0$ .
Solve for x: Solve for x by setting each factor equal to $0$ : $x + 7 = 0$ or $x + 6 = 0$ .
Find first x value: Find the first value of x: $x = -7$ .
Find second x value: Find the second value of x: $x = -6$ .
Substitute $x=-7$ for $y$ : Substitute $x = -7$ into the first equation to find $y$ : $y = -21(-7) - 14$ .
Calculate $y$ for $x=-7$ : Calculate $y$ for $x = -7$ : $y = 147 - 14$ , which simplifies to $y = 133$ .
Substitute $x=-6$ for $y$ : Substitute $x = -6$ into the first equation to find $y$ : $y = -21(-6) - 14$ .
Calculate $y$ for $x=-6$ : Calculate $y$ for $x = -6$ : $y = 126 - 14$ , which simplifies to $y = 112$ .
Write solution as coordinate points: Write the solution as coordinate points: $(-7, 133)$ and $(-6, 112)$ .