Solve the system of equations. y = x^2 - 2x + 37 y = 13x + 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: x^2 - 2x + 37 = 13x + 23.Rearrange to set to 0: Rearrange the equation to set it to 0: x^2 - 2x - 13x + 37 - 23 = 0.Combine like terms: Combine like terms: x^2 - 15x + 14 = 0.Factor the quadratic equation: Factor the quadratic equation: (x - 1)(x - 14) = 0.Solve for x: Solve for x by setting each factor equal to 0: x - 1 = 0 or x - 14 = 0.Find first x value: Find the first value of x: x = 1.Find second x value: Find the second value of x: x = 14.Substitute x=1 to find y: Substitute x = 1 into the first equation to find y: y = 1^2 - 2*1 + 37.Calculate y for x=1: Calculate y when x = 1: y = 1 - 2 + 37.Simplify to find first y: Simplify to find the first value of y: y = 36.Substitute x=14 to find y: Substitute x = 14 into the first equation to find y: y = 14^2 - 2*14 + 37.Calculate y for x=14: Calculate y when x = 14: y = 196 - 28 + 37.Simplify to find second y: Simplify to find the second value of y: y = 205.Write coordinates of solutions: Write the coordinates of the solutions: (1, 36) and (14, 205).

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Solve the system of equations. $\newline$ $y = x^2 - 2x + 37$ $\newline$ $y = 13x + 23$ $\newline$ 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 = x^2 - 2x + 37

\newline

y = 13x + 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: $x^2 - 2x + 37 = 13x + 23$ .
Rearrange to set to $0$ : Rearrange the equation to set it to $0$ : $x^2 - 2x - 13x + 37 - 23 = 0$ .
Combine like terms: Combine like terms: $x^2 - 15x + 14 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x - 1)(x - 14) = 0$ .
Solve for x: Solve for x by setting each factor equal to $0$ : $x - 1 = 0$ or $x - 14 = 0$ .
Find first x value: Find the first value of x: $x = 1$ .
Find second x value: Find the second value of x: $x = 14$ .
Substitute $x=1$ to find $y$ : Substitute $x = 1$ into the first equation to find $y$ : $y = 1^2 - 2\cdot1 + 37$ .
Calculate $y$ for $x=1$ : Calculate $y$ when $x = 1$ : $y = 1 - 2 + 37$ .
Simplify to find first y: Simplify to find the first value of $y$ : $y = 36$ .
Substitute $x=14$ to find $y$ : Substitute $x = 14$ into the first equation to find $y$ : $y = 14^2 - 2\times14 + 37$ .
Calculate $y$ for $x=14$ : Calculate $y$ when $x = 14$ : $y = 196 - 28 + 37$ .
Simplify to find second y: Simplify to find the second value of $y$ : $y = 205$ .
Write coordinates of solutions: Write the coordinates of the solutions: $(1, 36)$ and $(14, 205)$ .