Solve the system of equations. y = 7x^2 + 18x - 14 y = 18x - 7 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. 7x^2 + 18x - 14 = 18x - 7Subtract x Terms: Subtract 18x from both sides to get the x terms on one side. 7x^2 + 18x - 18x - 14 = 18x - 18x - 7 7x^2 - 14 = -7Add to Isolate: Add 7 to both sides to isolate the quadratic term. 7x^2 - 14 + 7 = -7 + 7 7x^2 - 7 = 0Factor Out: Factor out a 7 from the left side. 7(x^2 - 1) = 0Set Inside Equal: Set the inside of the parentheses equal to zero. x^2 - 1 = 0Factor Left Side: Factor the left side as a difference of squares. (x + 1)(x - 1) = 0Set Factors Equal: Set each factor equal to zero and solve for x. x + 1 = 0 or x - 1 = 0 x = -1 or x = 1Plug x = -1: Plug x = -1 into the second equation y = 18x - 7 to find the corresponding y value. y = 18(-1) - 7 y = -18 - 7 y = -25Plug x = 1: Plug x = 1 into the second equation y = 18x - 7 to find the corresponding y value. y = 18(1) - 7 y = 18 - 7 y = 11Write Coordinates: Write the coordinates in exact form. First Coordinate: (-1, -25) Second Coordinate: (1, 11)

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Solve the system of equations. $\newline$ $y = 7x^2 + 18x - 14$ $\newline$ $y = 18x - 7$ $\newline$ 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

Full solution

Q. Solve the system of equations.

\newline

y = 7x^2 + 18x - 14

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y = 18x - 7

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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 $y$ . $7x^2 + 18x - 14 = 18x - 7$
Subtract $x$ Terms: Subtract $18x$ from both sides to get the $x$ terms on one side. $\newline$ $7x^2 + 18x - 18x - 14 = 18x - 18x - 7$ $\newline$ $7x^2 - 14 = -7$
Add to Isolate: Add $7$ to both sides to isolate the quadratic term. $\newline$ $7x^2 - 14 + 7 = -7 + 7$ $\newline$ $7x^2 - 7 = 0$
Factor Out: Factor out a $7$ from the left side. $\newline$ $7(x^2 - 1) = 0$
Set Inside Equal: Set the inside of the parentheses equal to zero. $\newline$ $x^2 - 1 = 0$
Factor Left Side: Factor the left side as a difference of squares. $\newline$ $(x + 1)(x - 1) = 0$
Set Factors Equal: Set each factor equal to zero and solve for $x$ . $x + 1 = 0$ or $x - 1 = 0$ $x = -1$ or $x = 1$
Plug $x = -1$ : Plug $x = -1$ into the second equation $y = 18x - 7$ to find the corresponding $y$ value. $\newline$ $y = 18(-1) - 7$ $\newline$ $y = -18 - 7$ $\newline$ $y = -25$
Plug $x = 1$ : Plug $x = 1$ into the second equation $y = 18x - 7$ to find the corresponding $y$ value. $\newline$ $y = 18(1) - 7$ $\newline$ $y = 18 - 7$ $\newline$ $y = 11$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-1, -25)$ $\newline$ Second Coordinate: $(1, 11)$