Solve the system of equations. y = -23x - 26 y = x^2 - 36x + 4 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. This gives us -23x - 26 = x^2 - 36x + 4.Rearrange and Solve: Rearrange the equation to set it to zero and solve for x. This means we will add 23x to both sides and add 26 to both sides, resulting in x^2 - 36x + 23x + 4 + 26 = 0, which simplifies to x^2 - 13x + 30 = 0.Factor Quadratic Equation: Factor the quadratic equation x^2 - 13x + 30 = 0. The factors of 30 that add up to -13 are -10 and -3, so the factored form is (x - 10)(x - 3) = 0.Solve for x: Solve for x by setting each factor equal to zero. This gives us x - 10 = 0 or x - 3 = 0, which means x = 10 or x = 3.Substitute x Values: Substitute x = 10 into one of the original equations to find the corresponding y value. Using y = -23x - 26, we get y = -23(10) - 26, which simplifies to y = -230 - 26, resulting in y = -256.Find Corresponding y Values: Substitute x = 3 into one of the original equations to find the corresponding y value. Using y = -23x - 26, we get y = -23(3) - 26, which simplifies to y = -69 - 26, resulting in y = -95.

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Solve the system of equations. $\newline$ $y = -23x - 26$ $\newline$ $y = x^2 - 36x + 4$ $\newline$ 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 = -23x - 26

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y = x^2 - 36x + 4

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . This gives us $-23x - 26 = x^2 - 36x + 4$ .
Rearrange and Solve: Rearrange the equation to set it to zero and solve for $x$ . This means we will add $23x$ to both sides and add $26$ to both sides, resulting in $x^2 - 36x + 23x + 4 + 26 = 0$ , which simplifies to $x^2 - 13x + 30 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation $x^2 - 13x + 30 = 0$ . The factors of $30$ that add up to $-13$ are $-10$ and $-3$ , so the factored form is $(x - 10)(x - 3) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero. This gives us $x - 10 = 0$ or $x - 3 = 0$ , which means $x = 10$ or $x = 3$ .
Substitute x Values: Substitute $x = 10$ into one of the original equations to find the corresponding $y$ value. Using $y = -23x - 26$ , we get $y = -23(10) - 26$ , which simplifies to $y = -230 - 26$ , resulting in $y = -256$ .
Find Corresponding y Values: Substitute $x = 3$ into one of the original equations to find the corresponding y value. Using $y = -23x - 26$ , we get $y = -23(3) - 26$ , which simplifies to $y = -69 - 26$ , resulting in $y = -95$ .