Solve the system of equations. y = 24x - 33 y = x^2 + 50x - 8 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 since they are both equal to y. This gives us the equation 24x - 33 = x^2 + 50x - 8.Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This means we subtract 24x and add 33 to both sides, resulting in x^2 + 26x - 25 = 0.Factor quadratic equation: Factor the quadratic equation x^2 + 26x - 25. The factors of -25 that add up to 26 are 25 and 1. So the factored form is (x + 25)(x + 1) = 0.Solve for x: Solve for x by setting each factor equal to zero. This gives us x + 25 = 0 or x + 1 = 0, which means x = -25 or x = -1.Substitute x = -25: Substitute x = -25 into the first equation y = 24x - 33 to find the corresponding y value. This gives us y = 24(-25) - 33, which simplifies to y = -600 - 33, resulting in y = -633.Substitute x = -1: Substitute x = -1 into the first equation y = 24x - 33 to find the corresponding y value. This gives us y = 24(-1) - 33, which simplifies to y = -24 - 33, resulting in y = -57.

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Solve the system of equations. $\newline$ $y = 24x - 33$ $\newline$ $y = x^2 + 50x - 8$ $\newline$ 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 = 24x - 33

\newline

y = x^2 + 50x - 8

\newline

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 since they are both equal to $y$ . This gives us the equation $24x - 33 = x^2 + 50x - 8$ .
Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This means we subtract $24x$ and add $33$ to both sides, resulting in $x^2 + 26x - 25 = 0$ .
Factor quadratic equation: Factor the quadratic equation $x^2 + 26x - 25$ . The factors of $-25$ that add up to $26$ are $25$ and $1$ . So the factored form is $(x + 25)(x + 1) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero. This gives us $x + 25 = 0$ or $x + 1 = 0$ , which means $x = -25$ or $x = -1$ .
Substitute $x = -25$ : Substitute $x = -25$ into the first equation $y = 24x - 33$ to find the corresponding $y$ value. This gives us $y = 24(-25) - 33$ , which simplifies to $y = -600 - 33$ , resulting in $y = -633$ .
Substitute $x = -1$ : Substitute $x = -1$ into the first equation $y = 24x - 33$ to find the corresponding $y$ value. This gives us $y = 24(-1) - 33$ , which simplifies to $y = -24 - 33$ , resulting in $y = -57$ .