Question

solve the system of equations.
y = -17x + 50
y = x² - 17x - 50
write the coordinates in exact form. simplify all fractions and radicals.
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Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( -17x + 50 = x^2 - 17x - 50 \).

Step2: Simplify equation

Add \( 17x \) to both sides: \( 50 = x^2 - 50 \).

Step3: Solve for \( x \)

Add 50 to both sides: \( x^2 = 100 \), so \( x = \pm 10 \).

Step4: Find \( y \) for \( x = 10 \)

Substitute \( x = 10 \) into \( y = -17x + 50 \): \( y = -17(10) + 50 = -120 \).

Step5: Find \( y \) for \( x = -10 \)

Substitute \( x = -10 \) into \( y = -17x + 50 \): \( y = -17(-10) + 50 = 220 \).

Answer:

\((10, -120)\), \((-10, 220)\)