Solve the system of equations. y = x^2 + 10x - 4 y = 2x + 29 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into first equation: Substitute y from the second equation into the first equation: x^2 + 10x - 4 = 2x + 29.Rearrange to set to 0: Rearrange the equation to set it to 0: x^2 + 10x - 4 - 2x - 29 = 0.Simplify the equation: Simplify the equation: x^2 + 8x - 33 = 0.Factor the quadratic equation: Factor the quadratic equation: (x + 11)(x - 3) = 0.Solve for x: Solve for x: x = -11 or x = 3.Substitute x = -11: Substitute x = -11 into y = 2x + 29 to find y: y = 2(-11) + 29.Calculate y for x = -11: Calculate y for x = -11: y = -22 + 29.Simplify to find y: Simplify to find y: y = 7.Substitute x = 3: Substitute x = 3 into y = 2x + 29 to find y: y = 2(3) + 29.Calculate y for x = 3: Calculate y for x = 3: y = 6 + 29.Simplify to find y: Simplify to find y: y = 35.Write solution as coordinate points: Write the solution as coordinate points: (-11, 7) and (3, 35).

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Solve the system of equations. $\newline$ $y = x^2 + 10x - 4$ $\newline$ $y = 2x + 29$ $\newline$ 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 = x^2 + 10x - 4

\newline

y = 2x + 29

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation: $x^2 + 10x - 4 = 2x + 29$ .
Rearrange to set to $0$ : Rearrange the equation to set it to $0$ : $x^2 + 10x - 4 - 2x - 29 = 0$ .
Simplify the equation: Simplify the equation: $x^2 + 8x - 33 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x + 11)(x - 3) = 0$ .
Solve for x: Solve for x: $x = -11$ or $x = 3$ .
Substitute $x = -11$ : Substitute $x = -11$ into $y = 2x + 29$ to find $y$ : $y = 2(-11) + 29$ .
Calculate $y$ for $x = -11$ : Calculate $y$ for $x = -11$ : $y = -22 + 29$ .
Simplify to find y: Simplify to find y: $y = 7$ .
Substitute $x = 3$ : Substitute $x = 3$ into $y = 2x + 29$ to find $y$ : $y = 2(3) + 29$ .
Calculate $y$ for $x = 3$ : Calculate $y$ for $x = 3$ : $y = 6 + 29$ .
Simplify to find y: Simplify to find y: $y = 35$ .
Write solution as coordinate points: Write the solution as coordinate points: $(-11, 7)$ and $(3, 35)$ .