Solve the system of equations. y = -5x + 6 y = x^2 - 5x - 43 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation: y = x^2 - 5x - 43 becomes -5x + 6 = x^2 - 5x - 43.Simplify Equation: Simplify the equation: 0 = x^2 - 5x - 43 + 5x - 6.Combine Like Terms: Combine like terms: 0 = x^2 - 49.Add 49: Add 49 to both sides: 49 = x^2.Take Square Root: Take the square root of both sides: x = ±7.Substitute x for y: Substitute x back into the first equation to find y when x = 7: y = -5(7) + 6.Calculate y: Calculate y: y = -35 + 6.Simplify y: Simplify y: y = -29.Substitute x for y: Now substitute x back into the first equation to find y when x = -7: y = -5(-7) + 6.Calculate y: Calculate y: y = 35 + 6.Simplify y: Simplify y: y = 41.

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Solve the system of equations. $\newline$ $y = -5x + 6$ $\newline$ $y = x^2 - 5x - 43$ $\newline$ 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 = -5x + 6

\newline

y = x^2 - 5x - 43

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute y Equation: Substitute $y$ from the first equation into the second equation: $y = x^2 - 5x - 43$ becomes $-5x + 6 = x^2 - 5x - 43$ .
Simplify Equation: Simplify the equation: $0 = x^2 - 5x - 43 + 5x - 6$ .
Combine Like Terms: Combine like terms: $0 = x^2 - 49$ .
Add $49$ : Add $49$ to both sides: $49 = x^2$ .
Take Square Root: Take the square root of both sides: $x = \pm 7$ .
Substitute $x$ for $y$ : Substitute $x$ back into the first equation to find $y$ when $x = 7$ : $y = -5(7) + 6$ .
Calculate y: Calculate y: $y = -35 + 6$ .
Simplify $y$ : Simplify $y$ : $y = -29$ .
Substitute $x$ for $y$ : Now substitute $x$ back into the first equation to find $y$ when $x = -7$ : $y = -5(-7) + 6$ .
Calculate y: Calculate y: $y = 35 + 6$ .
Simplify $y$ : Simplify $y$ : $y = 41$ .