Solve the system of equations. y = 7x + 100 y = x^2 + 7x - 44 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 + 7x - 44 becomes 7x + 100 = x^2 + 7x - 44.Solve for x: Subtract 7x from both sides to get 100 = x^2 - 44.Find x: Add 44 to both sides to get x^2 = 144.Calculate y for x = 12: Take the square root of both sides to find x. This gives us x = 12 and x = -12, since both 12^2 and (-12)^2 equal 144.Calculate y for x = -12: Plug x = 12 into the first equation y = 7x + 100 to find the corresponding y value. This gives us y = 7(12) + 100.Calculate y for x = 12. y = 84 + 100, which is y = 184.Now plug x = -12 into the first equation y = 7x + 100 to find the corresponding y value. This gives us y = 7(-12) + 100.Calculate y for x = -12. y = -84 + 100, which is y = 16.

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Solve the system of equations. $\newline$ $y = 7x + 100$ $\newline$ $y = x^2 + 7x - 44$ $\newline$ 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 = 7x + 100

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y = x^2 + 7x - 44

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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: $y = x^2 + 7x - 44$ becomes $7x + 100 = x^2 + 7x - 44$ .
Solve for x: Subtract $7x$ from both sides to get $100 = x^2 - 44$ .
Find $x$ : Add $44$ to both sides to get $x^2 = 144$ .
Calculate $y$ for $x = 12$ : Take the square root of both sides to find $x$ . This gives us $x = 12$ and $x = -12$ , since both $12^2$ and $(-12)^2$ equal $144$ .
Calculate $y$ for $x = -12$ : Plug $x = 12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $y = 7(12) + 100$ .
Calculate $y$ for $x = -12$ : Plug $x = 12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $y = 7(12) + 100$ .Calculate $y$ for $x = 12$ . $y = 84 + 100$ , which is $y = 184$ .
Calculate $y$ for $x = -12$ : Plug $x = 12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $y = 7(12) + 100$ .Calculate $y$ for $x = 12$ . $y = 84 + 100$ , which is $y = 184$ .Now plug $x = -12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $x = -12$ $3$ .
Calculate $y$ for $x = -12$ : Plug $x = 12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $y = 7(12) + 100$ .Calculate $y$ for $x = 12$ . $y = 84 + 100$ , which is $y = 184$ .Now plug $x = -12$ into the first equation $y = 7x + 100$ to find the corresponding $y$ value. This gives us $x = -12$ $3$ .Calculate $y$ for $x = -12$ . $x = -12$ $6$ , which is $x = -12$ $7$ .