Solve the system of equations. y = x^2 - 37x - 42 y = -37x - 33 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. x^2 - 37x - 42 = -37x - 33Cancel Out Terms: Cancel out the -37x on both sides. x^2 - 42 = -33Isolate x^2: Add 42 to both sides to isolate x^2. x^2 = 9Solve for x: Take the square root of both sides to solve for x. x = 3 or x = -3Substitute x into Second Equation: Substitute x back into the second equation to find y. For x = 3: y = -37(3) - 33 = -111 - 33 = -144 For x = -3: y = -37(-3) - 33 = 111 - 33 = 78Write Coordinates: Write the coordinates in exact form. First Coordinate: (3, -144) Second Coordinate: (-3, 78)

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Solve the system of equations. $\newline$ $y = x^2 - 37x - 42$ $\newline$ $y = -37x - 33$ $\newline$ 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 - 37x - 42

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y = -37x - 33

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $x^2 - 37x - 42 = -37x - 33$
Cancel Out Terms: Cancel out the $-37x$ on both sides. $\newline$ $x^2 - 42 = -33$
Isolate $x^2$ : Add $42$ to both sides to isolate $x^2$ . $\newline$ $x^2 = 9$
Solve for x: Take the square root of both sides to solve for x. $\newline$ $x = 3$ or $x = -3$
Substitute $x$ into Second Equation: Substitute $x$ back into the second equation to find $y$ . $\newline$ For $x = 3$ : $y = -37(3) - 33 = -111 - 33 = -144$ $\newline$ For $x = -3$ : $y = -37(-3) - 33 = 111 - 33 = 78$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(3, -144)$ $\newline$ Second Coordinate: $(-3, 78)$