Solve the system of equations. y = 12x - 37 y = x^2 + 2x - 21 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. Since y = 12x - 37 and y = x^2 + 2x - 21, we can set them equal to each other: 12x - 37 = x^2 + 2x - 21.Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x: x^2 + 2x - 21 - 12x + 37 = 0, which simplifies to x^2 - 10x + 16 = 0.Factor the quadratic equation: Factor the quadratic equation: (x - 8)(x - 2) = 0.Solve for x: Solve for x by setting each factor equal to zero: x - 8 = 0 or x - 2 = 0. This gives us x = 8 or x = 2.Substitute x=8 to find y: Substitute x = 8 into the first equation to find y: y = 12(8) - 37, which simplifies to y = 96 - 37, so y = 59.Substitute x=2 to find y: Substitute x = 2 into the first equation to find y: y = 12(2) - 37, which simplifies to y = 24 - 37, so y = -13.

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Solve the system of equations. $\newline$ $y = 12x - 37$ $\newline$ $y = x^2 + 2x - 21$ $\newline$ 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 = 12x - 37

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y = x^2 + 2x - 21

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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. Since $y = 12x - 37$ and $y = x^2 + 2x - 21$ , we can set them equal to each other: $12x - 37 = x^2 + 2x - 21$ .
Rearrange and solve for x: Rearrange the equation to set it to zero and solve for $x$ : $x^2 + 2x - 21 - 12x + 37 = 0$ , which simplifies to $x^2 - 10x + 16 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x - 8)(x - 2) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 8 = 0$ or $x - 2 = 0$ . This gives us $x = 8$ or $x = 2$ .
Substitute $x=8$ to find $y$ : Substitute $x = 8$ into the first equation to find $y$ : $y = 12(8) - 37$ , which simplifies to $y = 96 - 37$ , so $y = 59$ .
Substitute $x=2$ to find $y$ : Substitute $x = 2$ into the first equation to find $y$ : $y = 12(2) - 37$ , which simplifies to $y = 24 - 37$ , so $y = -13$ .