Solve the system of equations. x = -3y + 5 x^2 + y^2 = 5 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute x into second equation: Substitute x from the first equation into the second equation. x = -3y + 5 x^2 + y^2 = 5 (-3y + 5)^2 + y^2 = 5Expand and simplify: Expand the squared term and simplify the equation. (-3y + 5)^2 + y^2 = 5 9y^2 - 30y + 25 + y^2 = 5 10y^2 - 30y + 25 = 5Set equation to zero: Subtract 5 from both sides to set the equation to zero. 10y^2 - 30y + 25 - 5 = 0 10y^2 - 30y + 20 = 0Divide and simplify: Divide the entire equation by 10 to simplify. 10y^2/10 - 30y/10 + 20/10 = 0 y^2 - 3y + 2 = 0Factor the quadratic equation: Factor the quadratic equation. y^2 - 3y + 2 = 0 (y - 2)(y - 1) = 0Solve for y: Solve for y by setting each factor equal to zero. y - 2 = 0 or y - 1 = 0 y = 2 or y = 1Substitute y into first equation: Substitute y back into the first equation to find x. For y = 2: x = -3(2) + 5 = -6 + 5 = -1 For y = 1: x = -3(1) + 5 = -3 + 5 = 2Write coordinates in exact form: Write the coordinates in exact form. First Coordinate: (-1, 2) Second Coordinate: (2, 1)

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Solve the system of equations. $\newline$ $x = -3y + 5$ $\newline$ $x^2 + y^2 = 5$ $\newline$ 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

x = -3y + 5

\newline

x^2 + y^2 = 5

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $x$ into second equation: Substitute $x$ from the first equation into the second equation. $\newline$ $x = -3y + 5$ $\newline$ $x^2 + y^2 = 5$ $\newline$ $(-3y + 5)^2 + y^2 = 5$
Expand and simplify: Expand the squared term and simplify the equation. $\newline$ $(-3y + 5)^2 + y^2 = 5$ $\newline$ $9y^2 - 30y + 25 + y^2 = 5$ $\newline$ $10y^2 - 30y + 25 = 5$
Set equation to zero: Subtract $5$ from both sides to set the equation to zero. $\newline$ $10y^2 - 30y + 25 - 5 = 0$ $\newline$ $10y^2 - 30y + 20 = 0$
Divide and simplify: Divide the entire equation by $10$ to simplify. $\newline$ $\frac{10y^2}{10} - \frac{30y}{10} + \frac{20}{10} = 0$ $\newline$ $y^2 - 3y + 2 = 0$
Factor the quadratic equation: Factor the quadratic equation. $\newline$ $y^2 - 3y + 2 = 0$ $\newline$ $(y - 2)(y - 1) = 0$
Solve for y: Solve for y by setting each factor equal to zero. $\newline$ $y - 2 = 0$ or $y - 1 = 0$ $\newline$ $y = 2$ or $y = 1$
Substitute $y$ into first equation: Substitute $y$ back into the first equation to find $x$ . $\newline$ For $y = 2$ : $x = -3(2) + 5 = -6 + 5 = -1$ $\newline$ For $y = 1$ : $x = -3(1) + 5 = -3 + 5 = 2$
Write coordinates in exact form: Write the coordinates in exact form. $\newline$ First Coordinate: $(-1, 2)$ $\newline$ Second Coordinate: $(2, 1)$