Solve the system of equations. y = x^2 + 34x - 11 y = 34x + 38 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. y = x^2 + 34x - 11 y = 34x + 38 So, x^2 + 34x - 11 = 34x + 38.Subtract to Simplify: Subtract 34x from both sides to simplify the equation. x^2 + 34x - 11 - 34x = 34x + 38 - 34x This simplifies to x^2 - 11 = 38.Add to Isolate x^2: Add 11 to both sides to isolate the x^2 term. x^2 - 11 + 11 = 38 + 11 This simplifies to x^2 = 49.Take Square Root: Take the square root of both sides to solve for x. √x^2 = √49 This gives us x = 7 and x = -7 (since both positive and negative roots are possible).Substitute x = 7: Substitute x = 7 into one of the original equations to find the corresponding y value. Using y = 34x + 38, we get y = 34(7) + 38. This simplifies to y = 238 + 38, which equals y = 276.Substitute x = -7: Substitute x = -7 into the same equation to find the corresponding y value. Using y = 34x + 38, we get y = 34(-7) + 38. This simplifies to y = -238 + 38, which equals y = -200.

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Solve the system of equations. $\newline$ $y = x^2 + 34x - 11$ $\newline$ $y = 34x + 38$ $\newline$ 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 + 34x - 11

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y = 34x + 38

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

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(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = x^2 + 34x - 11$ $y = 34x + 38$ So, $x^2 + 34x - 11 = 34x + 38$ .
Subtract to Simplify: Subtract $34x$ from both sides to simplify the equation. $\newline$ $x^2 + 34x - 11 - 34x = 34x + 38 - 34x$ $\newline$ This simplifies to $x^2 - 11 = 38$ .
Add to Isolate $x^2$ : Add $11$ to both sides to isolate the $x^2$ term. $\newline$ $x^2 - 11 + 11 = 38 + 11$ $\newline$ This simplifies to $x^2 = 49$ .
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \sqrt{49}$ This gives us $x = 7$ and $x = -7$ (since both positive and negative roots are possible).
Substitute $x = 7$ : Substitute $x = 7$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 34x + 38$ , we get $y = 34(7) + 38$ . $\newline$ This simplifies to $y = 238 + 38$ , which equals $y = 276$ .
Substitute $x = -7$ : Substitute $x = -7$ into the same equation to find the corresponding $y$ value. $\newline$ Using $y = 34x + 38$ , we get $y = 34(-7) + 38$ . $\newline$ This simplifies to $y = -238 + 38$ , which equals $y = -200$ .