Solve the system of equations. x^2 + y^2 = 20 x = -3y + 10 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute x: Substitute x from the second equation into the first equation. x^2 + y^2 = 20 x = -3y + 10 (-3y + 10)^2 + y^2 = 20Expand and simplify: Expand the squared term and simplify. (-3y + 10)^2 = 9y^2 - 60y + 100 9y^2 - 60y + 100 + y^2 = 20Combine like terms: Combine like terms. 10y^2 - 60y + 100 = 20 10y^2 - 60y + 80 = 0Divide and simplify: Divide the entire equation by 10 to simplify. y^2 - 6y + 8 = 0Factor quadratic equation: Factor the quadratic equation. (y - 4)(y - 2) = 0Solve for y: Solve for y by setting each factor equal to zero. y - 4 = 0 or y - 2 = 0 y = 4 or y = 2Substitute y into x: Substitute y back into x = -3y + 10 to find corresponding x values. For y = 4: x = -3(4) + 10 = -2 For y = 2: x = -3(2) + 10 = 4Write coordinates: Write the coordinates in exact form. First Coordinate: (-2, 4) Second Coordinate: (4, 2)

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Solve the system of equations. $\newline$ $x^2 + y^2 = 20$ $\newline$ $x = -3y + 10$ $\newline$ $\newline$ 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 = 20

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x = -3y + 10

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

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(______,______)

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(______,______)

Substitute $x$ : Substitute $x$ from the second equation into the first equation. $\newline$ $x^2 + y^2 = 20$ $\newline$ $x = -3y + 10$ $\newline$ $(-3y + 10)^2 + y^2 = 20$
Expand and simplify: Expand the squared term and simplify. $\newline$ $(-3y + 10)^2 = 9y^2 - 60y + 100$ $\newline$ $9y^2 - 60y + 100 + y^2 = 20$
Combine like terms: Combine like terms. $\newline$ $10y^2 - 60y + 100 = 20$ $\newline$ $10y^2 - 60y + 80 = 0$
Divide and simplify: Divide the entire equation by $10$ to simplify. $\newline$ $y^2 - 6y + 8 = 0$
Factor quadratic equation: Factor the quadratic equation. $\newline$ $(y - 4)(y - 2) = 0$
Solve for y: Solve for y by setting each factor equal to zero. $\newline$ $y - 4 = 0$ or $y - 2 = 0$ $\newline$ $y = 4$ or $y = 2$
Substitute $y$ into $x$ : Substitute $y$ back into $x = -3y + 10$ to find corresponding $x$ values. $\newline$ For $y = 4$ : $x = -3(4) + 10 = -2$ $\newline$ For $y = 2$ : $x = -3(2) + 10 = 4$
Write coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-2, 4)$ $\newline$ Second Coordinate: $(4, 2)$