Solve the system of equations. y = x^2 + 21x - 4 y = 22x + 26 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. This gives us x^2 + 21x - 4 = 22x + 26.Rearrange and Simplify: Rearrange the equation to set it to zero. Subtract 22x + 26 from both sides to get x^2 + 21x - 4 - 22x - 26 = 0. This simplifies to x^2 - x - 30 = 0.Factor Quadratic Equation: Factor the quadratic equation x^2 - x - 30. The factors of -30 that add up to -1 are -6 and +5. So the equation factors to (x - 6)(x + 5) = 0.Solve for x: Solve for x by setting each factor equal to zero. This gives us x - 6 = 0 and x + 5 = 0. Solving these gives us x = 6 and x = -5.Substitute x Values: Substitute x = 6 into one of the original equations to find the corresponding y value. Using y = 22x + 26, we get y = 22(6) + 26, which simplifies to y = 132 + 26, giving us y = 158.Find Corresponding y Values: Substitute x = -5 into one of the original equations to find the corresponding y value. Using y = 22x + 26, we get y = 22(-5) + 26, which simplifies to y = -110 + 26, giving us y = -84.

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Solve the system of equations. $\newline$ $y = x^2 + 21x - 4$ $\newline$ $y = 22x + 26$ $\newline$ 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 + 21x - 4

\newline

y = 22x + 26

\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 $y$ . This gives us $x^2 + 21x - 4 = 22x + 26$ .
Rearrange and Simplify: Rearrange the equation to set it to zero. Subtract $22x + 26$ from both sides to get $x^2 + 21x - 4 - 22x - 26 = 0$ . This simplifies to $x^2 - x - 30 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation $x^2 - x - 30$ . The factors of $-30$ that add up to $-1$ are $-6$ and $+5$ . So the equation factors to $(x - 6)(x + 5) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero. This gives us $x - 6 = 0$ and $x + 5 = 0$ . Solving these gives us $x = 6$ and $x = -5$ .
Substitute x Values: Substitute $x = 6$ into one of the original equations to find the corresponding $y$ value. Using $y = 22x + 26$ , we get $y = 22(6) + 26$ , which simplifies to $y = 132 + 26$ , giving us $y = 158$ .
Find Corresponding y Values: Substitute $x = -5$ into one of the original equations to find the corresponding y value. Using $y = 22x + 26$ , we get $y = 22(-5) + 26$ , which simplifies to $y = -110 + 26$ , giving us $y = -84$ .