Solve the system of equations. y = 14x - 26 y = 2x^2 + 14x - 34 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = 14x - 26 y = 2x^2 + 14x - 34 To find the intersection points, we set the two equations equal to each other. 14x - 26 = 2x^2 + 14x - 34Simplify Equation: Simplify the equation by subtracting 14x from both sides and adding 26 to both sides. 0 = 2x^2 + 14x - 34 - 14x + 26 0 = 2x^2 - 8Divide and Simplify: Divide the entire equation by 2 to simplify it further. 0 = x^2 - 4Factor Quadratic Equation: Factor the quadratic equation. x^2 - 4 = (x - 2)(x + 2)Solve for x: Solve for x by setting each factor equal to zero. (x - 2) = 0 or (x + 2) = 0 x = 2 or x = -2Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We'll use y = 14x - 26. For x = 2: y = 14(2) - 26 y = 28 - 26 y = 2Coordinate Calculation: For x = -2: y = 14(-2) - 26 y = -28 - 26 y = -54Write the coordinates in exact form. First Coordinate: (2, 2) Second Coordinate: (-2, -54)

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Solve the system of equations. $\newline$ $y = 14x - 26$ $\newline$ $y = 2x^2 + 14x - 34$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 1

Solve a system of linear and quadratic equations

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Q. Solve the system of equations.

\newline

y = 14x - 26

\newline

y = 2x^2 + 14x - 34

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = 14x - 26$ $\newline$ $y = 2x^2 + 14x - 34$ $\newline$ To find the intersection points, we set the two equations equal to each other. $\newline$ $14x - 26 = 2x^2 + 14x - 34$
Simplify Equation: Simplify the equation by subtracting $14x$ from both sides and adding $26$ to both sides. $\newline$ $0 = 2x^2 + 14x - 34 - 14x + 26$ $\newline$ $0 = 2x^2 - 8$
Divide and Simplify: Divide the entire equation by $2$ to simplify it further. $\newline$ $0 = x^2 - 4$
Factor Quadratic Equation: Factor the quadratic equation. $x^2 - 4 = (x - 2)(x + 2)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x - 2) = 0$ or $(x + 2) = 0$ $\newline$ $x = 2$ or $x = -2$
Find y-values: Find the corresponding y-values for each $x$ -value by substituting back into one of the original equations. We'll use $y = 14x - 26$ . For $x = 2$ : $y = 14(2) - 26$ $y = 28 - 26$ $y = 2$
Coordinate Calculation: For $x = -2$ : $\newline$ $y = 14(-2) - 26$ $\newline$ $y = -28 - 26$ $\newline$ $y = -54$
Coordinate Calculation: For $x = -2$ : $y = 14(-2) - 26$ $y = -28 - 26$ $y = -54$ Write the coordinates in exact form. $\text{First Coordinate: } (2, 2)$ $\text{Second Coordinate: } (-2, -54)$