Solve the system of equations. y = 7x - 16 y = x^2 + 29x + 24 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 to find the x-values where the two graphs intersect. This gives us the equation 7x - 16 = x^2 + 29x + 24.Rearrange and simplify equation: Rearrange the equation to set it to zero: x^2 + 29x + 24 - (7x - 16) = 0. This simplifies to x^2 + 22x + 40 = 0.Factor quadratic equation: Factor the quadratic equation x^2 + 22x + 40. The factors of 40 that add up to 22 are 2 and 20. So, the factored form is (x + 2)(x + 20) = 0.Find x-values: Set each factor equal to zero to find the x-values: x + 2 = 0 and x + 20 = 0. Solving these gives us x = -2 and x = -20.Substitute x = -2: Substitute x = -2 into the first equation y = 7x - 16 to find the corresponding y-value. This gives us y = 7(-2) - 16, which simplifies to y = -14 - 16, so y = -30.Substitute x = -20: Substitute x = -20 into the first equation y = 7x - 16 to find the corresponding y-value. This gives us y = 7(-20) - 16, which simplifies to y = -140 - 16, so y = -156.

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Solve the system of equations. $\newline$ $y = 7x - 16$ $\newline$ $y = x^2 + 29x + 24$ $\newline$ 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 = 7x - 16

\newline

y = x^2 + 29x + 24

\newline

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 to find the $x$ -values where the two graphs intersect. This gives us the equation $7x - 16 = x^2 + 29x + 24$ .
Rearrange and simplify equation: Rearrange the equation to set it to zero: $x^2 + 29x + 24 - (7x - 16) = 0$ . This simplifies to $x^2 + 22x + 40 = 0$ .
Factor quadratic equation: Factor the quadratic equation $x^2 + 22x + 40$ . The factors of $40$ that add up to $22$ are $2$ and $20$ . So, the factored form is $(x + 2)(x + 20) = 0$ .
Find x-values: Set each factor equal to zero to find the x-values: $x + 2 = 0$ and $x + 20 = 0$ . Solving these gives us $x = -2$ and $x = -20$ .
Substitute $x = -2$ : Substitute $x = -2$ into the first equation $y = 7x - 16$ to find the corresponding y-value. This gives us $y = 7(-2) - 16$ , which simplifies to $y = -14 - 16$ , so $y = -30$ .
Substitute $x = -20$ : Substitute $x = -20$ into the first equation $y = 7x - 16$ to find the corresponding y-value. This gives us $y = 7(-20) - 16$ , which simplifies to $y = -140 - 16$ , so $y = -156$ .