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Solve the system of equations. $\newline$ $y = 24x - 10$ $\newline$ $y = x^2 + 30x - 50$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve a nonlinear system of equations

Full solution

Q. Solve the system of equations.

\newline

y = 24x - 10

\newline

y = x^2 + 30x - 50

\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 $y$ . $\newline$ $y = 24x - 10$ $\newline$ $y = x^2 + 30x - 50$ $\newline$ So, $24x - 10 = x^2 + 30x - 50$
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ . $x^2 + 30x - 50 - (24x - 10) = 0$ $x^2 + 30x - 50 - 24x + 10 = 0$ $x^2 + 6x - 40 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $(x + 10)(x - 4) = 0$
Solve for x: Solve for the values of x. $\newline$ $x + 10 = 0$ or $x - 4 = 0$ $\newline$ $x = -10$ or $x = 4$
Substitute $x = -10$ : Substitute $x = -10$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = 24(-10) - 10$ $\newline$ $y = -240 - 10$ $\newline$ $y = -250$
Substitute $x = 4$ : Substitute $x = 4$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = 24(4) - 10$ $\newline$ $y = 96 - 10$ $\newline$ $y = 86$

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