Solve the system of equations. y = x^2 - 43x - 4 y = -43x + 45 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 43x - 4 y = -43x + 45 Set the two equations equal to each other to find the x-values where they intersect. x^2 - 43x - 4 = -43x + 45Simplify and Rearrange: Simplify the equation by adding 43x to both sides and subtracting 45 from both sides to get the quadratic equation in standard form. x^2 - 43x - 4 + 43x - 45 = -43x + 45 + 43x - 45 x^2 - 49 = 0Solve Quadratic Equation: Solve the quadratic equation for x. x^2 - 49 = 0 Factor the left side as a difference of squares. (x + 7)(x - 7) = 0Find Corresponding Y-Values: Set each factor equal to zero and solve for x. (x + 7) = 0 or (x - 7) = 0 x = -7 or x = 7Write Coordinates: Find the corresponding y-values for each x-value by substituting x into the second equation y = -43x + 45. For x = -7: y = -43(-7) + 45 y = 301 + 45 y = 346 For x = 7: y = -43(7) + 45 y = -301 + 45 y = -256Write the coordinates in exact form. First Coordinate: (-7, 346) Second Coordinate: (7, -256)

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Solve the system of equations. $\newline$ $y = x^2 - 43x - 4$ $\newline$ $y = -43x + 45$ $\newline$ 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 = x^2 - 43x - 4

\newline

y = -43x + 45

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 43x - 4$ $\newline$ $y = -43x + 45$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $x^2 - 43x - 4 = -43x + 45$
Simplify and Rearrange: Simplify the equation by adding $43x$ to both sides and subtracting $45$ from both sides to get the quadratic equation in standard form. $\newline$ $x^2 - 43x - 4 + 43x - 45 = -43x + 45 + 43x - 45$ $\newline$ $x^2 - 49 = 0$
Solve Quadratic Equation: Solve the quadratic equation for $x$ . $x^2 - 49 = 0$ Factor the left side as a difference of squares. $(x + 7)(x - 7) = 0$
Find Corresponding Y-Values: Set each factor equal to zero and solve for $x$ . $\$x + 7$ = $0$ \) or $\$x - 7$ = $0$ \) $x = -7$ or $x = 7$
Write Coordinates: Find the corresponding $y$ -values for each $x$ -value by substituting $x$ into the second equation $y = -43x + 45$ . For $x = -7$ : $y = -43(-7) + 45$ $y = 301 + 45$ $y = 346$ For $x = 7$ : $y = -43(7) + 45$ $x$ $0$ $x$ $1$
Write Coordinates: Find the corresponding $y$ -values for each $x$ -value by substituting $x$ into the second equation $y = -43x + 45$ . For $x = -7$ : $y = -43(-7) + 45$ $y = 301 + 45$ $y = 346$ For $x = 7$ : $y = -43(7) + 45$ $x$ $0$ $x$ $1$ Write the coordinates in exact form. First Coordinate: $x$ $2$ Second Coordinate: $x$ $3$