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Solve the system of equations. $\newline$ $y = x^2 + 45x - 27$ $\newline$ $y = 49x - 6$ $\newline$ 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 = x^2 + 45x - 27

\newline

y = 49x - 6

\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 $y$ . $y = x^2 + 45x - 27$ $y = 49x - 6$ So, $x^2 + 45x - 27 = 49x - 6$ .
Rearrange and Simplify: Rearrange the equation to set it to zero and simplify. $\newline$ $x^2 + 45x - 27 - 49x + 6 = 0$ $\newline$ $x^2 - 4x - 21 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 7)(x + 3) = 0$
Solve for x: Solve for the values of x. $\newline$ $x - 7 = 0$ or $x + 3 = 0$ $\newline$ $x = 7$ or $x = -3$
Substitute $x = 7$ : Substitute $x = 7$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = 49(7) - 6$ $\newline$ $y = 343 - 6$ $\newline$ $y = 337$
Substitute $x = -3$ : Substitute $x = -3$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = 49(-3) - 6$ $\newline$ $y = -147 - 6$ $\newline$ $y = -153$

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