Solve the system of equations. y = 29x - 50 y = x^2 + 43x - 37 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: x^2 + 43x - 37 = 29x - 50.Rearrange to set to zero: Rearrange the equation to set it to zero: x^2 + 43x - 29x - 37 + 50 = 0.Simplify the equation: Simplify the equation: x^2 + 14x + 13 = 0.Factor the quadratic equation: Factor the quadratic equation: (x + 1)(x + 13) = 0.Solve for x: Solve for x: x = -1 or x = -13.Substitute x = -1: Substitute x = -1 into the first equation to find y: y = 29(-1) - 50.Calculate y when x = -1: Calculate y when x = -1: y = -29 - 50.Simplify to find y: Simplify to find y: y = -79.Substitute x = -13: Substitute x = -13 into the first equation to find y: y = 29(-13) - 50.Calculate y when x = -13: Calculate y when x = -13: y = -377 - 50.Simplify to find y: Simplify to find y: y = -427.

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Solve the system of equations. $\newline$ $y = 29x - 50$ $\newline$ $y = x^2 + 43x - 37$ $\newline$ 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 = 29x - 50

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y = x^2 + 43x - 37

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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: $x^2 + 43x - 37 = 29x - 50$ .
Rearrange to set to zero: Rearrange the equation to set it to zero: $x^2 + 43x - 29x - 37 + 50 = 0$ .
Simplify the equation: Simplify the equation: $x^2 + 14x + 13 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x + 1)(x + 13) = 0$ .
Solve for x: Solve for x: $x = -1$ or $x = -13$ .
Substitute $x = -1$ : Substitute $x = -1$ into the first equation to find $y$ : $y = 29(-1) - 50$ .
Calculate $y$ when $x = -1$ : Calculate $y$ when $x = -1$ : $y = -29 - 50$ .
Simplify to find y: Simplify to find y: $y = -79$ .
Substitute $x = -13$ : Substitute $x = -13$ into the first equation to find $y$ : $y = 29(-13) - 50$ .
Calculate $y$ when $x = -13$ : Calculate $y$ when $x = -13$ : $y = -377 - 50$ .
Simplify to find y: Simplify to find y: $y = -427$ .