Solve the system of equations. y = -9x + 17 y = x^2 - 6x + 7 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the following system of equations: y = -9x + 17 y = x^2 - 6x + 7 To find the solution, we need to set the two equations equal to each other because they both equal y. -9x + 17 = x^2 - 6x + 7Rearrange Equation: Rearrange the equation to get a standard form of a quadratic equation by moving all terms to one side. 0 = x^2 - 6x + 9x + 7 - 17 0 = x^2 + 3x - 10Factor Quadratic: Factor the quadratic equation. We are looking for two numbers that multiply to -10 and add up to 3. These numbers are 5 and -2. 0 = (x + 5)(x - 2)Solve for x: Solve for x by setting each factor equal to zero. (x + 5) = 0 or (x - 2) = 0 x = -5 or x = 2Find y for x=-5: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y = -9x + 17. For x = -5: y = -9(-5) + 17 y = 45 + 17 y = 62Find y for x=2: Find the y-value for x = 2: y = -9(2) + 17 y = -18 + 17 y = -1Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the two graphs intersect, which are the x-values we found and their corresponding y-values. First Coordinate: (-5, 62) Second Coordinate: (2, -1)

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Solve the system of equations. $\newline$ $y = -9x + 17$ $\newline$ $y = x^2 - 6x + 7$ $\newline$ 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 = -9x + 17

\newline

y = x^2 - 6x + 7

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the following system of equations: $\newline$ $y = -9x + 17$ $\newline$ $y = x^2 - 6x + 7$ $\newline$ To find the solution, we need to set the two equations equal to each other because they both equal $y$ . $\newline$ $-9x + 17 = x^2 - 6x + 7$
Rearrange Equation: Rearrange the equation to get a standard form of a quadratic equation by moving all terms to one side. $\newline$ $0 = x^2 - 6x + 9x + 7 - 17$ $\newline$ $0 = x^2 + 3x - 10$
Factor Quadratic: Factor the quadratic equation. $\newline$ We are looking for two numbers that multiply to $-10$ and add up to $3$ . These numbers are $5$ and $-2$ . $\newline$ $0 = (x + 5)(x - 2)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x + 5) = 0$ or $(x - 2) = 0$ $\newline$ $x = -5$ or $x = 2$
Find $y$ for $x=-5$ : Find the corresponding $y$ -values for each $x$ -value by substituting back into one of the original equations. We can use $y = -9x + 17$ . $\newline$ For $x = -5$ : $\newline$ $y = -9(-5) + 17$ $\newline$ $y = 45 + 17$ $\newline$ $y = 62$
Find $y$ for $x=2$ : Find the $y$ -value for $x = 2$ :
$y = -9(2) + 17$
$y = -18 + 17$
$y = -1$
Write Coordinates: Write the coordinates in exact form. $\newline$ The solutions to the system of equations are the points where the two graphs intersect, which are the $x$ -values we found and their corresponding $y$ -values. $\newline$ First Coordinate: $(-5, 62)$ $\newline$ Second Coordinate: $(2, -1)$