Solve the system of equations. x^2 + y^2 = 325 y = -2x - 20 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. x^2 + (-2x - 20)^2 = 325Expand and simplify: Expand and simplify the equation. x^2 + (4x^2 + 80x + 400) = 325 5x^2 + 80x + 400 = 325Set equation to zero: Subtract 325 from both sides to set the equation to zero. 5x^2 + 80x + 75 = 0Divide and simplify: Divide the entire equation by 5 to simplify. x^2 + 16x + 15 = 0Factor the equation: Factor the quadratic equation. (x + 1)(x + 15) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 1 = 0 or x + 15 = 0 x = -1 or x = -15Substitute x into y: Substitute x values into y = -2x - 20 to find corresponding y values. For x = -1: y = -2(-1) - 20 = 2 - 20 = -18 For x = -15: y = -2(-15) - 20 = 30 - 20 = 10

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Solve the system of equations. $\newline$ $x^2 + y^2 = 325$ $\newline$ $y = -2x - 20$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,) $\newline$

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Algebra 2

Solve a system of linear and quadratic equations: circles

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Q. Solve the system of equations.

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x^2 + y^2 = 325

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y = -2x - 20

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

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(______,______)

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(______,______)

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Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation. $x^2 + (-2x - 20)^2 = 325$
Expand and simplify: Expand and simplify the equation. $\newline$ $x^2 + (4x^2 + 80x + 400) = 325$ $\newline$ $5x^2 + 80x + 400 = 325$
Set equation to zero: Subtract $325$ from both sides to set the equation to zero. $\newline$ $5x^2 + 80x + 75 = 0$
Divide and simplify: Divide the entire equation by $5$ to simplify. $\newline$ $x^2 + 16x + 15 = 0$
Factor the equation: Factor the quadratic equation. $\newline$ $(x + 1)(x + 15) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 1 = 0$ or $x + 15 = 0$ $\newline$ $x = -1$ or $x = -15$
Substitute $x$ into $y$ : Substitute $x$ values into $y = -2x - 20$ to find corresponding $y$ values. $\newline$ For $x = -1$ : $y = -2(-1) - 20 = 2 - 20 = -18$ $\newline$ For $x = -15$ : $y = -2(-15) - 20 = 30 - 20 = 10$