Solve the system of equations. y = -17x + 16 y = x^2 - 18x - 26 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: First, let's set the two equations equal to each other since they both equal y. -17x + 16 = x^2 - 18x - 26Move to One Side: Now, let's move everything to one side to set the equation to zero. x^2 - 18x + 17x - 26 - 16 = 0 x^2 - x - 42 = 0Factor Quadratic Equation: Next, we need to factor the quadratic equation. Looking for two numbers that multiply to -42 and add up to -1, we get -7 and 6. So, (x - 7)(x + 6) = 0Solve for x: Now, solve for x by setting each factor equal to zero. x - 7 = 0 or x + 6 = 0 So, x = 7 or x = -6Find Corresponding y Values: We have two values for x, let's find the corresponding y values. Substitute x = 7 into y = -17x + 16 to get y = -17(7) + 16 = -119 + 16 = -103. Substitute x = -6 into y = -17x + 16 to get y = -17(-6) + 16 = 102 + 16 = 118.Write Coordinates: Finally, we write the coordinates in exact form. The first coordinate is (7, -103). The second coordinate is (-6, 118).

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Solve the system of equations. $\newline$ $y = -17x + 16$ $\newline$ $y = x^2 - 18x - 26$ $\newline$ 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 = -17x + 16

\newline

y = x^2 - 18x - 26

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: First, let's set the two equations equal to each other since they both equal $y$ . $-17x + 16 = x^2 - 18x - 26$
Move to One Side: Now, let's move everything to one side to set the equation to zero. $\newline$ $x^2 - 18x + 17x - 26 - 16 = 0$ $\newline$ $x^2 - x - 42 = 0$
Factor Quadratic Equation: Next, we need to factor the quadratic equation. Looking for two numbers that multiply to $-42$ and add up to $-1$ , we get $-7$ and $6$ . So, $(x - 7)(x + 6) = 0$
Solve for x: Now, solve for $x$ by setting each factor equal to zero. $x - 7 = 0$ or $x + 6 = 0$ So, $x = 7$ or $x = -6$
Find Corresponding y Values: We have two values for $x$ , let's find the corresponding $y$ values. $\newline$ Substitute $x = 7$ into $y = -17x + 16$ to get $y = -17(7) + 16 = -119 + 16 = -103$ . $\newline$ Substitute $x = -6$ into $y = -17x + 16$ to get $y = -17(-6) + 16 = 102 + 16 = 118$ .
Write Coordinates: Finally, we write the coordinates in exact form. $\newline$ The first coordinate is $(7, -103)$ . $\newline$ The second coordinate is $(-6, 118)$ .