Solve the system of equations. y = -29x - 40 y = x^2 - 17x - 5 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -29x - 40 y = x^2 - 17x - 5 Set the two equations equal to each other to find the x-values where they intersect. -29x - 40 = x^2 - 17x - 5Rearrange to Standard Form: Rearrange the equation to get a standard form quadratic equation. x^2 - 17x - 5 + 29x + 40 = 0 x^2 + 12x + 35 = 0Factor Quadratic Equation: Factor the quadratic equation. In quadratic equation ax^2 + bx + c, the factors are of the form (x + m)(x + n), where b is the sum and c is the product of m and n respectively. x^2 + 12x + 35 = 0 (x + 7)(x + 5) = 0Solve for x: Solve for x. Set each factor equal to zero, and solve for x. (x + 7) = 0 or (x + 5) = 0 x = -7 or x = -5Find y for x=-7: Find the corresponding y-values for each x-value by substituting back into either of the original equations. We'll use y = -29x - 40. For x = -7: y = -29(-7) - 40 y = 203 - 40 y = 163Find y for x=-5: Find the corresponding y-value for x = -5: y = -29(-5) - 40 y = 145 - 40 y = 105Write Coordinates: Write the coordinates in exact form. First Coordinate: (-7, 163) Second Coordinate: (-5, 105)

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Solve the system of equations. $\newline$ $y = -29x - 40$ $\newline$ $y = x^2 - 17x - 5$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a system of linear and quadratic equations: parabolas

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Q. Solve the system of equations.

\newline

y = -29x - 40

\newline

y = x^2 - 17x - 5

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = -29x - 40$ $\newline$ $y = x^2 - 17x - 5$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $-29x - 40 = x^2 - 17x - 5$
Rearrange to Standard Form: Rearrange the equation to get a standard form quadratic equation. $\newline$ $x^2 - 17x - 5 + 29x + 40 = 0$ $\newline$ $x^2 + 12x + 35 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ In quadratic equation $ax^2 + bx + c$ , the factors are of the form $(x + m)(x + n)$ , where $b$ is the sum and $c$ is the product of $m$ and $n$ respectively. $\newline$ $x^2 + 12x + 35 = 0$ $\newline$ $(x + 7)(x + 5) = 0$
Solve for x: Solve for x. $\newline$ Set each factor equal to zero, and solve for x. $\newline$ $(x + 7) = 0$ or $(x + 5) = 0$ $\newline$ $x = -7$ or $x = -5$
Find $y$ for $x=-7$ : Find the corresponding $y$ -values for each $x$ -value by substituting back into either of the original equations. We'll use $y = -29x - 40$ . For $x = -7$ : $y = -29(-7) - 40$ $y = 203 - 40$ $y = 163$
Find $y$ for $x=-5$ : Find the corresponding $y$ -value for $x = -5$ :
$y = -29(-5) - 40$
$y = 145 - 40$
$y = 105$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-7, 163)$ $\newline$ Second Coordinate: $(-5, 105)$