Solve the system of equations. y = 36x + 13 y = x^2 + 46x + 29 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 = 36x + 13 y = x^2 + 46x + 29 So, 36x + 13 = x^2 + 46x + 29.Rearrange and Solve: Rearrange the equation to set it to zero and solve for x. 0 = x^2 + 46x + 29 - 36x - 13 0 = x^2 + 10x + 16Factor Quadratic Equation: Factor the quadratic equation. 0 = (x + 2)(x + 8)Solve for x: Solve for x by setting each factor equal to zero. x + 2 = 0 or x + 8 = 0 This gives us x = -2 or x = -8.Substitute x Values: Substitute x = -2 into one of the original equations to solve for y. Using y = 36x + 13: y = 36(-2) + 13 y = -72 + 13 y = -59Write Coordinate Points: Substitute x = -8 into the same original equation to solve for y. Using y = 36x + 13: y = 36(-8) + 13 y = -288 + 13 y = -275Write the solution as coordinate points. The coordinate points are (-2, -59) and (-8, -275).

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Solve the system of equations. $\newline$ $y = 36x + 13$ $\newline$ $y = x^2 + 46x + 29$ $\newline$ 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 = 36x + 13

\newline

y = x^2 + 46x + 29

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = 36x + 13$ $y = x^2 + 46x + 29$ So, $36x + 13 = x^2 + 46x + 29$ .
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ . $0 = x^2 + 46x + 29 - 36x - 13$ $0 = x^2 + 10x + 16$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $0 = (x + 2)(x + 8)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 2 = 0$ or $x + 8 = 0$ $\newline$ This gives us $x = -2$ or $x = -8$ .
Substitute $x$ Values: Substitute $x = -2$ into one of the original equations to solve for $y$ . Using $y = 36x + 13$ : $y = 36(-2) + 13$ $y = -72 + 13$ $y = -59$
Write Coordinate Points: Substitute $x = -8$ into the same original equation to solve for $y$ . Using $y = 36x + 13$ : $y = 36(-8) + 13$ $y = -288 + 13$ $y = -275$
Write Coordinate Points: Substitute $x = -8$ into the same original equation to solve for $y$ . Using $y = 36x + 13$ : $y = 36(-8) + 13$ $y = -288 + 13$ $y = -275$ Write the solution as coordinate points. The coordinate points are $(-2, -59)$ and $(-8, -275)$ .