Solve the system of equations. y = 17x + 22 y = x^2 + 15x - 2 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = 17x + 22 y = x^2 + 15x - 2 Set the two equations equal to each other to find the x-values where they intersect. 17x + 22 = x^2 + 15x - 2Rearrange and Identify: Rearrange the equation to set it to zero and identify the standard form of the quadratic equation. x^2 + 15x - 2 - 17x - 22 = 0 x^2 - 2x - 24 = 0Factor Quadratic Equation: Factor the quadratic equation to find the values of x. In the 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 - 2x - 24 = (x - 6)(x + 4)Solve for x: Solve for x by setting each factor equal to zero. (x - 6) = 0 or (x + 4) = 0 x = 6 or x = -4Find y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. For x = 6, substitute into y = 17x + 22: y = 17(6) + 22 y = 102 + 22 y = 124 For x = -4, substitute into y = 17x + 22: y = 17(-4) + 22 y = -68 + 22 y = -46Write Coordinates: Write the coordinates in exact form. The first coordinate is (6, 124). The second coordinate is (-4, -46).

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Solve the system of equations. $\newline$ $y = 17x + 22$ $\newline$ $y = x^2 + 15x - 2$ $\newline$ 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 = 17x + 22

\newline

y = x^2 + 15x - 2

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = 17x + 22$ $\newline$ $y = x^2 + 15x - 2$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $17x + 22 = x^2 + 15x - 2$
Rearrange and Identify: Rearrange the equation to set it to zero and identify the standard form of the quadratic equation. $\newline$ $x^2 + 15x - 2 - 17x - 22 = 0$ $\newline$ $x^2 - 2x - 24 = 0$
Factor Quadratic Equation: Factor the quadratic equation to find the values of $x$ . In the 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. $x^2 - 2x - 24 = (x - 6)(x + 4)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x - 6) = 0$ or $(x + 4) = 0$ $\newline$ $x = 6$ or $x = -4$
Find y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. $\newline$ For $x = 6$ , substitute into $y = 17x + 22$ : $\newline$ $y = 17(6) + 22$ $\newline$ $y = 102 + 22$ $\newline$ $y = 124$ $\newline$ For $x = -4$ , substitute into $y = 17x + 22$ : $\newline$ $y = 17(-4) + 22$ $\newline$ $y = -68 + 22$ $\newline$ $y = -46$
Write Coordinates: Write the coordinates in exact form. $\newline$ The first coordinate is $(6, 124)$ . $\newline$ The second coordinate is $(-4, -46)$ .