Solve the system of equations. x^2 + y^2 = 580 y = -3x + 30 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 + (-3x + 30)^2 = 580Expand and simplify: Expand and simplify the equation. x^2 + 9x^2 - 180x + 900 = 580Combine like terms: Combine like terms. 10x^2 - 180x + 900 - 580 = 0Further simplify: Simplify the equation further. 10x^2 - 180x + 320 = 0Divide by 10: Divide the entire equation by 10 to simplify. x^2 - 18x + 32 = 0Factor the quadratic equation: Factor the quadratic equation. (x - 16)(x - 2) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 16 = 0 or x - 2 = 0Find x-values: Find the two x-values. x = 16 or x = 2Substitute x into y: Substitute x-values into y = -3x + 30 to find corresponding y-values. For x = 16: y = -3(16) + 30 = -18 For x = 2: y = -3(2) + 30 = 24Write coordinates: Write the coordinates in exact form. First Coordinate: (16, -18) Second Coordinate: (2, 24)

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Solve the system of equations. $\newline$ $x^2 + y^2 = 580$ $\newline$ $y = -3x + 30$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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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 = 580

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y = -3x + 30

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

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(______,______)

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(______,______)

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation. $x^2 + (-3x + 30)^2 = 580$
Expand and simplify: Expand and simplify the equation. $x^2 + 9x^2 - 180x + 900 = 580$
Combine like terms: Combine like terms. $10x^2 - 180x + 900 - 580 = 0$
Further simplify: Simplify the equation further. $10x^2 - 180x + 320 = 0$
Divide by $10$ : Divide the entire equation by $10$ to simplify. $x^2 - 18x + 32 = 0$
Factor the quadratic equation: Factor the quadratic equation. $\newline$ $(x - 16)(x - 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 16 = 0$ or $x - 2 = 0$
Find x-values: Find the two x-values. $x = 16$ or $x = 2$
Substitute $x$ into $y$ : Substitute $x$ -values into $y = -3x + 30$ to find corresponding $y$ -values. $\newline$ For $x = 16$ : $y = -3(16) + 30 = -18$ $\newline$ For $x = 2$ : $y = -3(2) + 30 = 24$
Write coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(16, -18)$ $\newline$ Second Coordinate: $(2, 24)$