Solve the system of equations. y = 38x + 41 y = x^2 + 38x - 40 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y in second equation: Substitute y from the first equation into the second equation since they are both equal to y. This gives us the equation 38x + 41 = x^2 + 38x - 40.Simplify the equation: Simplify the equation by subtracting 38x from both sides and subtracting 41 from both sides to get 0 = x^2 - 40 - 41.Further simplify to x^2 - 81: Further simplify the equation to get 0 = x^2 - 81.Factor the quadratic equation: Factor the quadratic equation to find the values of x. This gives us (x - 9)(x + 9) = 0.Solve for x: Set each factor equal to zero and solve for x. This gives us x = 9 and x = -9.Substitute x = 9: Substitute x = 9 into the first equation y = 38x + 41 to find the corresponding value of y. This gives us y = 38(9) + 41.Calculate y when x = 9: Calculate the value of y when x = 9. This gives us y = 342 + 41, which simplifies to y = 383.Substitute x = -9: Substitute x = -9 into the first equation y = 38x + 41 to find the corresponding value of y. This gives us y = 38(-9) + 41.Calculate y when x = -9: Calculate the value of y when x = -9. This gives us y = -342 + 41, which simplifies to y = -301.

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Solve the system of equations. $\newline$ $y = 38x + 41$ $\newline$ $y = x^2 + 38x - 40$ $\newline$ 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 = 38x + 41

\newline

y = x^2 + 38x - 40

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ in second equation: Substitute $y$ from the first equation into the second equation since they are both equal to $y$ . This gives us the equation $38x + 41 = x^2 + 38x - 40$ .
Simplify the equation: Simplify the equation by subtracting $38x$ from both sides and subtracting $41$ from both sides to get $0 = x^2 - 40 - 41$ .
Further simplify to $x^2 - 81$ : Further simplify the equation to get $0 = x^2 - 81$ .
Factor the quadratic equation: Factor the quadratic equation to find the values of $x$ . This gives us $(x - 9)(x + 9) = 0$ .
Solve for $x$ : Set each factor equal to zero and solve for $x$ . This gives us $x = 9$ and $x = -9$ .
Substitute $x = 9$ : Substitute $x = 9$ into the first equation $y = 38x + 41$ to find the corresponding value of $y$ . This gives us $y = 38(9) + 41$ .
Calculate $y$ when $x = 9$ : Calculate the value of $y$ when $x = 9$ . This gives us $y = 342 + 41$ , which simplifies to $y = 383$ .
Substitute $x = -9$ : Substitute $x = -9$ into the first equation $y = 38x + 41$ to find the corresponding value of $y$ . This gives us $y = 38(-9) + 41$ .
Calculate $y$ when $x = -9$ : Calculate the value of $y$ when $x = -9$ . This gives us $y = -342 + 41$ , which simplifies to $y = -301$ .