Solve the system of equations. y = 6x + 15 y = x^2 + 6x - 49 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into second equation: Substitute y from the first equation into the second equation: x^2 + 6x - 49 = 6x + 15.Simplify the equation: Simplify the equation: x^2 + 6x - 6x - 49 - 15 = 0, which simplifies to x^2 - 64 = 0.Factor the equation: Factor the equation: (x + 8)(x - 8) = 0.Find values of x: Find the values of x: x + 8 = 0 or x - 8 = 0, so x = -8 or x = 8.Substitute x = -8 for y: Substitute x = -8 into the first equation to find y: y = 6(-8) + 15, which simplifies to y = -48 + 15, so y = -33.Substitute x = 8 for y: Substitute x = 8 into the first equation to find y: y = 6(8) + 15, which simplifies to y = 48 + 15, so y = 63.

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Solve the system of equations. $\newline$ $y = 6x + 15$ $\newline$ $y = x^2 + 6x - 49$ $\newline$ 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 = 6x + 15

\newline

y = x^2 + 6x - 49

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into second equation: Substitute $y$ from the first equation into the second equation: $x^2 + 6x - 49 = 6x + 15$ .
Simplify the equation: Simplify the equation: $x^2 + 6x - 6x - 49 - 15 = 0$ , which simplifies to $x^2 - 64 = 0$ .
Factor the equation: Factor the equation: $(x + 8)(x - 8) = 0$ .
Find values of x: Find the values of x: $x + 8 = 0$ or $x - 8 = 0$ , so $x = -8$ or $x = 8$ .
Substitute $x = -8$ for $y$ : Substitute $x = -8$ into the first equation to find $y$ : $y = 6(-8) + 15$ , which simplifies to $y = -48 + 15$ , so $y = -33$ .
Substitute $x = 8$ for $y$ : Substitute $x = 8$ into the first equation to find $y$ : $y = 6(8) + 15$ , which simplifies to $y = 48 + 15$ , so $y = 63$ .