Solve the system of equations. y = -3x - 25 x^2 + y^2 = 125 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y: Substitute y from the first equation into the second equation. y = -3x - 25 x^2 + y^2 = 125 x^2 + (-3x - 25)^2 = 125Expand and simplify: Expand and simplify the equation. x^2 + (9x^2 + 150x + 625) = 125 10x^2 + 150x + 625 = 125Subtract 125: Subtract 125 from both sides to set the equation to zero. 10x^2 + 150x + 625 - 125 = 0 10x^2 + 150x + 500 = 0Divide and simplify: Divide the entire equation by 10 to simplify. x^2 + 15x + 50 = 0Factor the equation: Factor the quadratic equation. (x + 10)(x + 5) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 10 = 0 or x + 5 = 0 x = -10 or x = -5Find y-values: Find the corresponding y-values for each x-value. For x = -10: y = -3(-10) - 25 = 30 - 25 = 5 For x = -5: y = -3(-5) - 25 = 15 - 25 = -10Write coordinates: Write the coordinates in exact form. First Coordinate: (-10, 5) Second Coordinate: (-5, -10)

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Solve the system of equations. $\newline$ $y = -3x - 25$ $\newline$ $x^2 + y^2 = 125$ $\newline$ $\newline$ 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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y = -3x - 25

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x^2 + y^2 = 125

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

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(______,______)

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(______,______)

Substitute $y$ : Substitute $y$ from the first equation into the second equation. $\newline$ $y = -3x - 25$ $\newline$ $x^2 + y^2 = 125$ $\newline$ $x^2 + (-3x - 25)^2 = 125$
Expand and simplify: Expand and simplify the equation. $\newline$ $x^2 + (9x^2 + 150x + 625) = 125$ $\newline$ $10x^2 + 150x + 625 = 125$
Subtract $125$ : Subtract $125$ from both sides to set the equation to zero. $\newline$ $10x^2 + 150x + 625 - 125 = 0$ $\newline$ $10x^2 + 150x + 500 = 0$
Divide and simplify: Divide the entire equation by $10$ to simplify. $\newline$ $x^2 + 15x + 50 = 0$
Factor the equation: Factor the quadratic equation. $\newline$ $(x + 10)(x + 5) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 10 = 0$ or $x + 5 = 0$ $\newline$ $x = -10$ or $x = -5$
Find y-values: Find the corresponding y-values for each x-value. $\newline$ For $x = -10$ : $y = -3(-10) - 25 = 30 - 25 = 5$ $\newline$ For $x = -5$ : $y = -3(-5) - 25 = 15 - 25 = -10$
Write coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-10, 5)$ $\newline$ Second Coordinate: $(-5, -10)$