Solve the system of equations. y = x^2 + 42x - 44 y = 42x + 77 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 + 42x - 44 y = 42x + 77 So, x^2 + 42x - 44 = 42x + 77Subtract to Simplify: Subtract 42x from both sides to get the quadratic equation in terms of x. x^2 + 42x - 44 - 42x = 42x + 77 - 42x This simplifies to: x^2 - 44 = 77Add to Isolate x^2: Add 44 to both sides to isolate the x^2 term. x^2 - 44 + 44 = 77 + 44 This simplifies to: x^2 = 121Take Square Root: Take the square root of both sides to solve for x. √(x^2) = ±√121 This gives us: x = ±11Substitute x Values: Substitute x = 11 into one of the original equations to find the corresponding y value. Using y = 42x + 77, we get: y = 42(11) + 77 y = 462 + 77 y = 539Write as Coordinate Points: Substitute x = -11 into the same equation to find the corresponding y value. y = 42(-11) + 77 y = -462 + 77 y = -385Write the solution as coordinate points. The coordinate points are (11, 539) and (-11, -385).

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Solve the system of equations. $\newline$ $y = x^2 + 42x - 44$ $\newline$ $y = 42x + 77$ $\newline$ 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 + 42x - 44

\newline

y = 42x + 77

\newline

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 $y$ . $\newline$ $y = x^2 + 42x - 44$ $\newline$ $y = 42x + 77$ $\newline$ So, $x^2 + 42x - 44 = 42x + 77$
Subtract to Simplify: Subtract $42x$ from both sides to get the quadratic equation in terms of $x$ . $\newline$ $x^2 + 42x - 44 - 42x = 42x + 77 - 42x$ $\newline$ This simplifies to: $\newline$ $x^2 - 44 = 77$
Add to Isolate $x^2$ : Add $44$ to both sides to isolate the $x^2$ term. $\newline$ $x^2 - 44 + 44 = 77 + 44$ $\newline$ This simplifies to: $\newline$ $x^2 = 121$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \pm\sqrt{121}$ This gives us: $x = \pm11$
Substitute x Values: Substitute $x = 11$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 42x + 77$ , we get: $\newline$ $y = 42(11) + 77$ $\newline$ $y = 462 + 77$ $\newline$ $y = 539$
Write as Coordinate Points: Substitute $x = -11$ into the same equation to find the corresponding $y$ value. $\newline$ $y = 42(-11) + 77$ $\newline$ $y = -462 + 77$ $\newline$ $y = -385$
Write as Coordinate Points: Substitute $x = -11$ into the same equation to find the corresponding $y$ value. $y = 42(-11) + 77$ $y = -462 + 77$ $y = -385$ Write the solution as coordinate points. $\newline$ The coordinate points are $(11, 539)$ and $(-11, -385)$ .