Solve the system of equations. x^2 + y^2 = 425 x = 4y Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute x = 4y: Substitute x = 4y into x^2 + y^2 = 425. (4y)^2 + y^2 = 425 16y^2 + y^2 = 425Combine like terms: Combine like terms. 17y^2 = 425Divide and solve for y^2: Divide both sides by 17 to solve for y^2. y^2 = 425 / 17 y^2 = 25Find y: Take the square root of both sides to find y. y = ±√25 y = ±5Substitute back to find x: Substitute y back into x = 4y to find x. x = 4(5) and x = 4(-5) x = 20 and x = -20Write coordinates: Write the coordinates in exact form. First Coordinate: (20, 5) Second Coordinate: (-20, -5)

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Solve the system of equations. $\newline$ $x^2 + y^2 = 425$ $\newline$ $x = 4y$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Math Problems

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 = 425

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x = 4y

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

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(______,______)

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(______,______)

Substitute $x = 4y$ : Substitute $x = 4y$ into $x^2 + y^2 = 425$ .
$(4y)^2 + y^2 = 425$
$16y^2 + y^2 = 425$
Combine like terms: Combine like terms. $17y^2 = 425$
Divide and solve for $y^2$ : Divide both sides by $17$ to solve for $y^2$ . $y^2 = \frac{425}{17}$ $y^2 = 25$
Find $y$ : Take the square root of both sides to find $y$ . $\newline$ $y = \pm\sqrt{25}$ $\newline$ $y = \pm5$
Substitute back to find $x$ : Substitute $y$ back into $x = 4y$ to find $x$ .
$x = 4(5)$ and $x = 4(-5)$
$x = 20$ and $x = -20$
Write coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(20, 5)$ $\newline$ Second Coordinate: $(-20, -5)$