Solve the system of equations. y = -3x + 3 y = x^2 + 10x + 33 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 to find x. This gives us -3x + 3 = x^2 + 10x + 33.Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This gives us x^2 + 10x + 33 + 3x - 3 = 0, which simplifies to x^2 + 13x + 30 = 0.Factor the quadratic equation: Factor the quadratic equation. The factors of 30 that add up to 13 are 3 and 10, so the factored form is (x + 3)(x + 10) = 0.Solve for x: Set each factor equal to zero and solve for x. This gives us x + 3 = 0 or x + 10 = 0, which means x = -3 or x = -10.Substitute x = -3: Substitute x = -3 into the first equation to find the corresponding y value. This gives us y = -3(-3) + 3, which simplifies to y = 9 + 3 and then y = 12.Substitute x = -10: Substitute x = -10 into the first equation to find the corresponding y value. This gives us y = -3(-10) + 3, which simplifies to y = 30 + 3 and then y = 33.

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Solve the system of equations. $\newline$ $y = -3x + 3$ $\newline$ $y = x^2 + 10x + 33$ $\newline$ 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 = -3x + 3

\newline

y = x^2 + 10x + 33

\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 to find $x$ . This gives us $-3x + 3 = x^2 + 10x + 33$ .
Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This gives us $x^2 + 10x + 33 + 3x - 3 = 0$ , which simplifies to $x^2 + 13x + 30 = 0$ .
Factor the quadratic equation: Factor the quadratic equation. The factors of $30$ that add up to $13$ are $3$ and $10$ , so the factored form is $(x + 3)(x + 10) = 0$ .
Solve for x: Set each factor equal to zero and solve for x. This gives us $x + 3 = 0$ or $x + 10 = 0$ , which means $x = -3$ or $x = -10$ .
Substitute $x = -3$ : Substitute $x = -3$ into the first equation to find the corresponding $y$ value. This gives us $y = -3(-3) + 3$ , which simplifies to $y = 9 + 3$ and then $y = 12$ .
Substitute $x = -10$ : Substitute $x = -10$ into the first equation to find the corresponding $y$ value. This gives us $y = -3(-10) + 3$ , which simplifies to $y = 30 + 3$ and then $y = 33$ .