Solve the system of equations. y = 21x + 41 y = x^2 + 21x - 23 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: y = x^2 + 21x - 23 becomes 21x + 41 = x^2 + 21x - 23.Subtract 21x: Subtract 21x from both sides to get 41 = x^2 - 23.Add 23: Add 23 to both sides to find x^2 = 64.Take square root: Take the square root of both sides to find x = ±8.Substitute x=8 into y: Substitute x = 8 into y = 21x + 41 to find y. This gives us y = 21(8) + 41.Calculate y for x=8: Calculate y for x = 8: y = 168 + 41, which is y = 209.Substitute x=-8 into y: Now substitute x = -8 into y = 21x + 41 to find y. This gives us y = 21(-8) + 41.Calculate y for x=-8: Calculate y for x = -8: y = -168 + 41, which is y = -127.

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Solve the system of equations. $\newline$ $y = 21x + 41$ $\newline$ $y = x^2 + 21x - 23$ $\newline$ 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 = 21x + 41

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y = x^2 + 21x - 23

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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: $y = x^2 + 21x - 23$ becomes $21x + 41 = x^2 + 21x - 23$ .
Subtract $21x$ : Subtract $21x$ from both sides to get $41 = x^2 - 23$ .
Add $23$ : Add $23$ to both sides to find $x^2 = 64$ .
Take square root: Take the square root of both sides to find $x = \pm 8$ .
Substitute $x=8$ into $y$ : Substitute $x = 8$ into $y = 21x + 41$ to find $y$ . This gives us $y = 21(8) + 41$ .
Calculate $y$ for $x=8$ : Calculate $y$ for $x = 8$ : $y = 168 + 41$ , which is $y = 209$ .
Substitute $x=-8$ into $y$ : Now substitute $x = -8$ into $y = 21x + 41$ to find $y$ . This gives us $y = 21(-8) + 41$ .
Calculate $y$ for $x=-8$ : Calculate $y$ for $x = -8$ : $y = -168 + 41$ , which is $y = -127$ .