Solve the system of equations. y = x^2 - 50x - 50 y = -50x + 31 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the following system of equations: y = x^2 - 50x - 50 y = -50x + 31 To find the solution, we will set the two equations equal to each other since they both equal y. x^2 - 50x - 50 = -50x + 31Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. x^2 - 50x - 50 + 50x - 31 = -50x + 31 + 50x - 31 x^2 - 81 = 0Solve for x: Solve the quadratic equation for x. x^2 = 81 Take the square root of both sides. x = ±sqrt(81) x = ±9Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y = -50x + 31. For x = 9: y = -50(9) + 31 y = -450 + 31 y = -419Find Second y-value: Find the y-value for the second x-value. For x = -9: y = -50(-9) + 31 y = 450 + 31 y = 481Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the two graphs intersect. First Coordinate: (9, -419) Second Coordinate: (-9, 481)

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Solve the system of equations. $\newline$ $y = x^2 - 50x - 50$ $\newline$ $y = -50x + 31$ $\newline$ 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 - 50x - 50

\newline

y = -50x + 31

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the following system of equations: $\newline$ $y = x^2 - 50x - 50$ $\newline$ $y = -50x + 31$ $\newline$ To find the solution, we will set the two equations equal to each other since they both equal $y$ . $\newline$ $x^2 - 50x - 50 = -50x + 31$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $x^2 - 50x - 50 + 50x - 31 = -50x + 31 + 50x - 31$ $\newline$ $x^2 - 81 = 0$
Solve for x: Solve the quadratic equation for x. $\newline$ $x^2 = 81$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm\sqrt{81}$ $\newline$ $x = \pm9$
Find y-values: Find the corresponding y-values for each $x$ -value by substituting back into one of the original equations. We can use $y = -50x + 31$ . For $x = 9$ : $y = -50(9) + 31$ $y = -450 + 31$ $y = -419$
Find Second y-value: Find the y-value for the second x-value. $\newline$ For $x = -9$ : $\newline$ $y = -50(-9) + 31$ $\newline$ $y = 450 + 31$ $\newline$ $y = 481$
Write Coordinates: Write the coordinates in exact form. $\newline$ The solutions to the system of equations are the points where the two graphs intersect. $\newline$ First Coordinate: $(9, -419)$ $\newline$ Second Coordinate: $(-9, 481)$