Solve the system of equations. y = x^2 + 20x - 25 y = 22x + 23 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 + 20x - 25 = 22x + 23Subtract and Simplify: Subtract 22x + 23 from both sides to set the equation to zero. x^2 + 20x - 25 - 22x - 23 = 0Combine Like Terms: Combine like terms. x^2 - 2x - 48 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 8)(x + 6) = 0Solve for x: Set each factor equal to zero and solve for x. x - 8 = 0 and x + 6 = 0 x = 8 and x = -6Substitute x = 8: Substitute x = 8 into the first equation to find y. y = 8^2 + 20(8) - 25 y = 64 + 160 - 25 y = 199Substitute x = -6: Substitute x = -6 into the first equation to find y. y = (-6)^2 + 20(-6) - 25 y = 36 - 120 - 25 y = -109Write Coordinates: Write the coordinates in exact form. First Coordinate: (8, 199) Second Coordinate: (-6, -109)

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Solve the system of equations. $\newline$ $y = x^2 + 20x - 25$ $\newline$ $y = 22x + 23$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 1

Solve a system of linear and quadratic equations

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Q. Solve the system of equations.

\newline

y = x^2 + 20x - 25

\newline

y = 22x + 23

\newline

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 $y$ . $x^2 + 20x - 25 = 22x + 23$
Subtract and Simplify: Subtract $22x + 23$ from both sides to set the equation to zero. $\newline$ $x^2 + 20x - 25 - 22x - 23 = 0$
Combine Like Terms: Combine like terms. $\newline$ $x^2 - 2x - 48 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 8)(x + 6) = 0$
Solve for $x$ : Set each factor equal to zero and solve for $x$ . $x - 8 = 0$ and $x + 6 = 0$ $x = 8$ and $x = -6$
Substitute $x = 8$ : Substitute $x = 8$ into the first equation to find $y$ . $y = 8^2 + 20(8) - 25$ $y = 64 + 160 - 25$ $y = 199$
Substitute $x = -6$ : Substitute $x = -6$ into the first equation to find $y$ . $\newline$ $y = (-6)^2 + 20(-6) - 25$ $\newline$ $y = 36 - 120 - 25$ $\newline$ $y = -109$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(8, 199)$ $\newline$ Second Coordinate: $(-6, -109)$