Solve the system of equations. y = 2x - 15 x^2 + y^2 = 170 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation. y = 2x - 15 x^2 + y^2 = 170 x^2 + (2x - 15)^2 = 170Expand and Simplify: Expand the squared term and simplify the equation. x^2 + (2x - 15)(2x - 15) = 170 x^2 + 4x^2 - 60x + 225 = 170 5x^2 - 60x + 225 = 170Set Equation to Zero: Subtract 170 from both sides to set the equation to zero. 5x^2 - 60x + 225 - 170 = 0 5x^2 - 60x + 55 = 0Divide and Simplify: Divide the entire equation by 5 to simplify. x^2 - 12x + 11 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 11)(x - 1) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 11 = 0 or x - 1 = 0 x = 11 or x = 1Find y-values: Find the corresponding y-values using the first equation y = 2x - 15. For x = 11: y = 2(11) - 15 = 22 - 15 = 7 For x = 1: y = 2(1) - 15 = 2 - 15 = -13Write Coordinates: Write the coordinates in exact form. First Coordinate: (11, 7) Second Coordinate: (1, -13)

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Solve the system of equations. $\newline$ $y = 2x - 15$ $\newline$ $x^2 + y^2 = 170$ $\newline$ 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 - 15

\newline

x^2 + y^2 = 170

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute y Equation: Substitute $y$ from the first equation into the second equation. $\newline$ $y = 2x - 15$ $\newline$ $x^2 + y^2 = 170$ $\newline$ $x^2 + (2x - 15)^2 = 170$
Expand and Simplify: Expand the squared term and simplify the equation. $\newline$ $x^2 + (2x - 15)(2x - 15) = 170$ $\newline$ $x^2 + 4x^2 - 60x + 225 = 170$ $\newline$ $5x^2 - 60x + 225 = 170$
Set Equation to Zero: Subtract $170$ from both sides to set the equation to zero. $\newline$ $5x^2 - 60x + 225 - 170 = 0$ $\newline$ $5x^2 - 60x + 55 = 0$
Divide and Simplify: Divide the entire equation by $5$ to simplify. $\newline$ $x^2 - 12x + 11 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 11)(x - 1) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 11 = 0$ or $x - 1 = 0$ $\newline$ $x = 11$ or $x = 1$
Find y-values: Find the corresponding y-values using the first equation $y = 2x - 15$ . For $x = 11$ : $y = 2(11) - 15 = 22 - 15 = 7$ For $x = 1$ : $y = 2(1) - 15 = 2 - 15 = -13$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(11, 7)$ $\newline$ Second Coordinate: $(1, -13)$