Solve the system of equations. y = 35x - 29 y = x^2 + 22x + 7 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 = 35x - 29 and y = x^2 + 22x + 7, we can set them equal to each other: 35x - 29 = x^2 + 22x + 7.Rearrange and Solve for x: Rearrange the equation to set it to zero and solve for x: x^2 + 22x + 7 - 35x + 29 = 0, which simplifies to x^2 - 13x + 36 = 0.Factor Quadratic Equation: Factor the quadratic equation: (x - 4)(x - 9) = 0.Solve for x: Solve for x by setting each factor equal to zero: x - 4 = 0 or x - 9 = 0. This gives us x = 4 or x = 9.Substitute x = 4: Substitute x = 4 into the first equation y = 35x - 29 to find the corresponding value of y: y = 35(4) - 29, which simplifies to y = 140 - 29, so y = 111.Substitute x = 9: Substitute x = 9 into the first equation y = 35x - 29 to find the corresponding value of y: y = 35(9) - 29, which simplifies to y = 315 - 29, so y = 286.Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (4, 111) and (9, 286).

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Solve the system of equations. $\newline$ $y = 35x - 29$ $\newline$ $y = x^2 + 22x + 7$ $\newline$ 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 - 29

\newline

y = x^2 + 22x + 7

\newline

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 $y = 35x - 29$ and $y = x^2 + 22x + 7$ , we can set them equal to each other: $35x - 29 = x^2 + 22x + 7$ .
Rearrange and Solve for x: Rearrange the equation to set it to zero and solve for x: $x^2 + 22x + 7 - 35x + 29 = 0$ , which simplifies to $x^2 - 13x + 36 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation: $(x - 4)(x - 9) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 4 = 0$ or $x - 9 = 0$ . This gives us $x = 4$ or $x = 9$ .
Substitute $x = 4$ : Substitute $x = 4$ into the first equation $y = 35x - 29$ to find the corresponding value of $y$ : $y = 35(4) - 29$ , which simplifies to $y = 140 - 29$ , so $y = 111$ .
Substitute $x = 9$ : Substitute $x = 9$ into the first equation $y = 35x - 29$ to find the corresponding value of $y$ : $y = 35(9) - 29$ , which simplifies to $y = 315 - 29$ , so $y = 286$ .
Write Coordinate Points: Write the solution as coordinate points. The coordinate points are $(4, 111)$ and $(9, 286)$ .