Solve the system of equations. y = x^2 + 33x + 49 y = 47x + 16 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into first equation: Substitute y from the second equation into the first equation to find x. This gives us x^2 + 33x + 49 = 47x + 16.Rearrange to set to zero: Rearrange the equation to set it to zero: x^2 + 33x + 49 - 47x - 16 = 0. This simplifies to x^2 - 14x + 33 = 0.Factor the quadratic equation: Factor the quadratic equation x^2 - 14x + 33 = 0. The factors of 33 that add up to -14 are -11 and -3. So the equation factors to (x - 11)(x - 3) = 0.Solve for x: Solve for x by setting each factor equal to zero: x - 11 = 0 or x - 3 = 0. This gives us x = 11 or x = 3.Substitute x=11 into second equation: Substitute x = 11 into the second equation y = 47x + 16 to find the corresponding y value. This gives us y = 47(11) + 16.Calculate y for x=11: Calculate the y value for x = 11: y = 517 + 16, which simplifies to y = 533.Substitute x=3 into second equation: Substitute x = 3 into the second equation y = 47x + 16 to find the corresponding y value. This gives us y = 47(3) + 16.Calculate y for x=3: Calculate the y value for x = 3: y = 141 + 16, which simplifies to y = 157.

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Solve the system of equations. $\newline$ $y = x^2 + 33x + 49$ $\newline$ $y = 47x + 16$ $\newline$ 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 + 33x + 49

\newline

y = 47x + 16

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation to find $x$ . This gives us $x^2 + 33x + 49 = 47x + 16$ .
Rearrange to set to zero: Rearrange the equation to set it to zero: $x^2 + 33x + 49 - 47x - 16 = 0$ . This simplifies to $x^2 - 14x + 33 = 0$ .
Factor the quadratic equation: Factor the quadratic equation $x^2 - 14x + 33 = 0$ . The factors of $33$ that add up to $-14$ are $-11$ and $-3$ . So the equation factors to $(x - 11)(x - 3) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 11 = 0$ or $x - 3 = 0$ . This gives us $x = 11$ or $x = 3$ .
Substitute $x=11$ into second equation: Substitute $x = 11$ into the second equation $y = 47x + 16$ to find the corresponding $y$ value. This gives us $y = 47(11) + 16$ .
Calculate $y$ for $x=11$ : Calculate the $y$ value for $x = 11$ : $y = 517 + 16$ , which simplifies to $y = 533$ .
Substitute $x=3$ into second equation: Substitute $x = 3$ into the second equation $y = 47x + 16$ to find the corresponding $y$ value. This gives us $y = 47(3) + 16$ .
Calculate $y$ for $x=3$ : Calculate the $y$ value for $x = 3$ : $y = 141 + 16$ , which simplifies to $y = 157$ .