Solve the system of equations. y = 2x - 20 x^2 + y^2 = 260 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y: Substitute y from the first equation into the second equation. y = 2x - 20 x^2 + y^2 = 260 x^2 + (2x - 20)^2 = 260Expand and simplify: Expand and simplify the equation. x^2 + (2x - 20)(2x - 20) = 260 x^2 + 4x^2 - 80x + 400 = 260 5x^2 - 80x + 400 = 260Subtract 260: Subtract 260 from both sides to set the equation to zero. 5x^2 - 80x + 400 - 260 = 0 5x^2 - 80x + 140 = 0Divide and simplify: Divide the entire equation by 5 to simplify. x^2 - 16x + 28 = 0Factor the equation: Factor the quadratic equation. (x - 14)(x - 2) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 14 = 0 or x - 2 = 0 x = 14 or x = 2Find corresponding y values: Find the corresponding y values for each x. For x = 14: y = 2(14) - 20 = 28 - 20 = 8 For x = 2: y = 2(2) - 20 = 4 - 20 = -16Write coordinates: Write the coordinates in exact form. First Coordinate: (14, 8) Second Coordinate: (2, -16)

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Solve the system of equations. $\newline$ $y = 2x - 20$ $\newline$ $x^2 + y^2 = 260$ $\newline$ 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.

\newline

y = 2x - 20

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x^2 + y^2 = 260

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ : Substitute $y$ from the first equation into the second equation. $\newline$ $y = 2x - 20$ $\newline$ $x^2 + y^2 = 260$ $\newline$ $x^2 + (2x - 20)^2 = 260$
Expand and simplify: Expand and simplify the equation. $\newline$ $x^2 + (2x - 20)(2x - 20) = 260$ $\newline$ $x^2 + 4x^2 - 80x + 400 = 260$ $\newline$ $5x^2 - 80x + 140 = 260$
Subtract $260$ : Subtract $260$ from both sides to set the equation to zero. $\newline$ $5x^2 - 80x + 400 - 260 = 0$ $\newline$ $5x^2 - 80x + 140 = 0$
Divide and simplify: Divide the entire equation by $5$ to simplify. $x^2 - 16x + 28 = 0$
Factor the equation: Factor the quadratic equation. $\newline$ $(x - 14)(x - 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 14 = 0$ or $x - 2 = 0$ $\newline$ $x = 14$ or $x = 2$
Find corresponding y values: Find the corresponding y values for each $x$ . $\newline$ For $x = 14$ : $y = 2(14) - 20 = 28 - 20 = 8$ $\newline$ For $x = 2$ : $y = 2(2) - 20 = 4 - 20 = -16$
Write coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(14, 8)$ $\newline$ Second Coordinate: $(2, -16)$