Solve the system of equations. y = 13x - 44 y = x^2 + 33x - 8 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Since both equations are equal to y, we can set them equal to each other to find x. This gives us the equation 13x - 44 = x^2 + 33x - 8.Rearrange and Solve: Rearrange the equation to set it to zero and solve for x. This means subtracting 13x and adding 44 to both sides, resulting in 0 = x^2 + 20x - 36.Factor Quadratic Equation: Factor the quadratic equation x^2 + 20x - 36. The factors of -36 that add up to 20 are 26 and -6. This gives us (x + 26)(x - 6) = 0.Solve for x: Set each factor equal to zero and solve for x. This gives us two solutions: x + 26 = 0, which means x = -26, and x - 6 = 0, which means x = 6.Substitute x = -26: Substitute x = -26 into one of the original equations to find the corresponding y value. Using y = 13x - 44, we get y = 13(-26) - 44, which simplifies to y = -338 - 44, resulting in y = -382.Substitute x = 6: Substitute x = 6 into one of the original equations to find the corresponding y value. Using y = 13x - 44, we get y = 13(6) - 44, which simplifies to y = 78 - 44, resulting in y = 34.

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Solve the system of equations. $\newline$ $y = 13x - 44$ $\newline$ $y = x^2 + 33x - 8$ $\newline$ 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 = 13x - 44

\newline

y = x^2 + 33x - 8

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Since both equations are equal to $y$ , we can set them equal to each other to find $x$ . This gives us the equation $13x - 44 = x^2 + 33x - 8$ .
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ . This means subtracting $13x$ and adding $44$ to both sides, resulting in $0 = x^2 + 20x - 36$ .
Factor Quadratic Equation: Factor the quadratic equation $x^2 + 20x - 36$ . The factors of $-36$ that add up to $20$ are $26$ and $-6$ . This gives us $(x + 26)(x - 6) = 0$ .
Solve for x: Set each factor equal to zero and solve for x. This gives us two solutions: $x + 26 = 0$ , which means $x = -26$ , and $x - 6 = 0$ , which means $x = 6$ .
Substitute $x = -26$ : Substitute $x = -26$ into one of the original equations to find the corresponding $y$ value. Using $y = 13x - 44$ , we get $y = 13(-26) - 44$ , which simplifies to $y = -338 - 44$ , resulting in $y = -382$ .
Substitute $x = 6$ : Substitute $x = 6$ into one of the original equations to find the corresponding $y$ value. Using $y = 13x - 44$ , we get $y = 13(6) - 44$ , which simplifies to $y = 78 - 44$ , resulting in $y = 34$ .