Solve the system of equations. y = 21x - 36 y = x^2 + 9x - 1 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation. Since y = 21x - 36 and y = x^2 + 9x - 1, we can set them equal to each other: 21x - 36 = x^2 + 9x - 1.Rearrange and Solve: Rearrange the equation to set it to zero and solve for x: x^2 + 9x - 1 - 21x + 36 = 0, which simplifies to x^2 - 12x + 35 = 0.Factor Quadratic Equation: Factor the quadratic equation: (x - 7)(x - 5) = 0.Solve for x: Solve for x by setting each factor equal to zero: x - 7 = 0 or x - 5 = 0. This gives us two solutions for x: x = 7 and x = 5.Substitute x = 7: Substitute x = 7 into the first equation y = 21x - 36 to find the corresponding value of y: y = 21(7) - 36, which simplifies to y = 147 - 36, so y = 111.Substitute x = 5: Substitute x = 5 into the first equation y = 21x - 36 to find the corresponding value of y: y = 21(5) - 36, which simplifies to y = 105 - 36, so y = 69.Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (7, 111) and (5, 69).

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Solve the system of equations. $\newline$ $y = 21x - 36$ $\newline$ $y = x^2 + 9x - 1$ $\newline$ 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 - 36

\newline

y = x^2 + 9x - 1

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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. Since $y = 21x - 36$ and $y = x^2 + 9x - 1$ , we can set them equal to each other: $21x - 36 = x^2 + 9x - 1$ .
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ : $x^2 + 9x - 1 - 21x + 36 = 0$ , which simplifies to $x^2 - 12x + 35 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation: $(x - 7)(x - 5) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 7 = 0$ or $x - 5 = 0$ . This gives us two solutions for $x$ : $x = 7$ and $x = 5$ .
Substitute $x = 7$ : Substitute $x = 7$ into the first equation $y = 21x - 36$ to find the corresponding value of $y$ : $y = 21(7) - 36$ , which simplifies to $y = 147 - 36$ , so $y = 111$ .
Substitute $x = 5$ : Substitute $x = 5$ into the first equation $y = 21x - 36$ to find the corresponding value of $y$ : $y = 21(5) - 36$ , which simplifies to $y = 105 - 36$ , so $y = 69$ .
Write Coordinate Points: Write the solution as coordinate points. The coordinate points are $(7, 111)$ and $(5, 69)$ .