Solve the system of equations. y = x^2 + 23x - 50 y = 23x + 71 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. y = x^2 + 23x - 50 y = 23x + 71 So, x^2 + 23x - 50 = 23x + 71Subtract to Standard Form: Subtract 23x from both sides to get the quadratic equation in standard form. x^2 + 23x - 50 - 23x = 23x + 71 - 23x This simplifies to: x^2 - 50 = 71Add to Isolate x^2: Add 50 to both sides to isolate the x^2 term. x^2 - 50 + 50 = 71 + 50 This simplifies to: x^2 = 121Take Square Root: Take the square root of both sides to solve for x. √(x^2) = ±√121 This gives us: x = ±11Substitute x Values: Substitute x = 11 into one of the original equations to find the corresponding y value. Using y = 23x + 71, we get: y = 23(11) + 71 y = 253 + 71 y = 324Find Corresponding y: Substitute x = -11 into the same equation to find the other corresponding y value. y = 23(-11) + 71 y = -253 + 71 y = -182Write as Coordinate Points: Write the solution as coordinate points. The coordinate points are (11, 324) and (-11, -182).

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Solve the system of equations. $\newline$ $y = x^2 + 23x - 50$ $\newline$ $y = 23x + 71$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a nonlinear system of equations

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Q. Solve the system of equations.

\newline

y = x^2 + 23x - 50

\newline

y = 23x + 71

\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 $y$ . $y = x^2 + 23x - 50$ $y = 23x + 71$ So, $x^2 + 23x - 50 = 23x + 71$
Subtract to Standard Form: Subtract $23x$ from both sides to get the quadratic equation in standard form. $\newline$ $x^2 + 23x - 50 - 23x = 23x + 71 - 23x$ $\newline$ This simplifies to: $\newline$ $x^2 - 50 = 71$
Add to Isolate $x^2$ : Add $50$ to both sides to isolate the $x^2$ term. $\newline$ $x^2 - 50 + 50 = 71 + 50$ $\newline$ This simplifies to: $\newline$ $x^2 = 121$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \pm\sqrt{121}$ This gives us: $x = \pm11$
Substitute x Values: Substitute $x = 11$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 23x + 71$ , we get: $\newline$ $y = 23(11) + 71$ $\newline$ $y = 253 + 71$ $\newline$ $y = 324$
Find Corresponding y: Substitute $x = -11$ into the same equation to find the other corresponding y value. $\newline$ $y = 23(-11) + 71$ $\newline$ $y = -253 + 71$ $\newline$ $y = -182$
Write as Coordinate Points: Write the solution as coordinate points. $\newline$ The coordinate points are $(11, 324)$ and $(-11, -182)$ .