Solve the system of equations. y = 5x^2 + 13x - 10 y = 13x + 10 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. 5x^2 + 13x - 10 = 13x + 10Subtract and Set to Zero: Subtract 13x + 10 from both sides to move all terms to one side and set the equation to zero. 5x^2 + 13x - 10 - 13x - 10 = 13x + 10 - 13x - 10 5x^2 - 20 = 0Add to Isolate Quadratic Term: Add 20 to both sides to isolate the quadratic term. 5x^2 - 20 + 20 = 0 + 20 5x^2 = 20Divide to Solve for x^2: Divide both sides by 5 to solve for x^2. 5x^2 / 5 = 20 / 5 x^2 = 4Take Square Root for x: Take the square root of both sides to solve for x. sqrt(x^2) = sqrt(4) x = 2 or x = -2Substitute x = 2: Substitute x = 2 into the second equation to find the corresponding y value. y = 13(2) + 10 y = 26 + 10 y = 36Substitute x = -2: Substitute x = -2 into the second equation to find the corresponding y value. y = 13(-2) + 10 y = -26 + 10 y = -16Write Coordinates: Write the coordinates in exact form. First Coordinate: (2, 36) Second Coordinate: (-2, -16)

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Solve the system of equations. $\newline$ $y = 5x^2 + 13x - 10$ $\newline$ $y = 13x + 10$ $\newline$ 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: parabolas

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Q. Solve the system of equations.

\newline

y = 5x^2 + 13x - 10

\newline

y = 13x + 10

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

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(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $5x^2 + 13x - 10 = 13x + 10$
Subtract and Set to Zero: Subtract $13x + 10$ from both sides to move all terms to one side and set the equation to zero. $\newline$ $5x^2 + 13x - 10 - 13x - 10 = 13x + 10 - 13x - 10$ $\newline$ $5x^2 - 20 = 0$
Add to Isolate Quadratic Term: Add $20$ to both sides to isolate the quadratic term. $\newline$ $5x^2 - 20 + 20 = 0 + 20$ $\newline$ $5x^2 = 20$
Divide to Solve for $x^2$ : Divide both sides by $5$ to solve for $x^2$ . $\frac{5x^2}{5} = \frac{20}{5}$ $x^2 = 4$
Take Square Root for x: Take the square root of both sides to solve for x. $\newline$ $\sqrt{x^2} = \sqrt{4}$ $\newline$ $x = 2$ or $x = -2$
Substitute $x = 2$ : Substitute $x = 2$ into the second equation to find the corresponding $y$ value. $\newline$ $y = 13(2) + 10$ $\newline$ $y = 26 + 10$ $\newline$ $y = 36$
Substitute $x = -2$ : Substitute $x = -2$ into the second equation to find the corresponding $y$ value. $y = 13(-2) + 10$ $y = -26 + 10$ $y = -16$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(2, 36)$ $\newline$ Second Coordinate: $(-2, -16)$