Solve the system of equations. y = 33x + 11 y = x^2 + 33x - 25 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y: Substitute y from the first equation into the second equation: y = x^2 + 33x - 25 becomes 33x + 11 = x^2 + 33x - 25.Subtract and simplify: Subtract 33x from both sides to get 11 = x^2 - 25.Add and solve for x: Add 25 to both sides to solve for x: 11 + 25 = x^2, which simplifies to 36 = x^2.Take square root: Take the square root of both sides to find x: x = ±√36.Calculate x values: Since √36 is 6, we have x = ±6.Calculate y for x = 6: Plug x = 6 into the first equation to find y: y = 33(6) + 11.Calculate y for x = -6: Calculate y for x = 6: y = 198 + 11, which simplifies to y = 209.Find solution points: Now plug x = -6 into the first equation to find y: y = 33(-6) + 11.Calculate y for x = -6: y = -198 + 11, which simplifies to y = -187.The solution to the system of equations is the points where the two graphs intersect, which are (6, 209) and (-6, -187).

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Solve the system of equations. $\newline$ $y = 33x + 11$ $\newline$ $y = x^2 + 33x - 25$ $\newline$ 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 = 33x + 11

\newline

y = x^2 + 33x - 25

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ : Substitute $y$ from the first equation into the second equation: $y = x^2 + 33x - 25$ becomes $33x + 11 = x^2 + 33x - 25$ .
Subtract and simplify: Subtract $33x$ from both sides to get $11 = x^2 - 25$ .
Add and solve for x: Add $25$ to both sides to solve for $x$ : $11 + 25 = x^2$ , which simplifies to $36 = x^2$ .
Take square root: Take the square root of both sides to find $x$ : $x = \pm\sqrt{36}$ .
Calculate $x$ values: Since $\sqrt{36}$ is $6$ , we have $x = \pm 6$ .
Calculate $y$ for $x = 6$ : Plug $x = 6$ into the first equation to find $y$ : $y = 33(6) + 11$ .
Calculate $y$ for $x = -6$ : Calculate $y$ for $x = 6$ : $y = 198 + 11$ , which simplifies to $y = 209$ .
Find solution points: Now plug $x = -6$ into the first equation to find $y$ : $y = 33(-6) + 11$ .
Find solution points: Now plug $x = -6$ into the first equation to find $y$ : $y = 33(-6) + 11$ .Calculate $y$ for $x = -6$ : $y = -198 + 11$ , which simplifies to $y = -187$ .
Find solution points: Now plug $x = -6$ into the first equation to find $y$ : $y = 33(-6) + 11$ .Calculate $y$ for $x = -6$ : $y = -198 + 11$ , which simplifies to $y = -187$ .The solution to the system of equations is the points where the two graphs intersect, which are $(6, 209)$ and $(-6, -187)$ .