Question

solve the system of equations.
y = 34x + 100
y = x² + 34x - 44
write the coordinates in exact form. simplify all fractions and radicals.
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Explanation:

Step1: Set the equations equal

Since both equations equal \( y \), set \( 34x + 100 = x^2 + 34x - 44 \).

Step2: Simplify the equation

Subtract \( 34x \) from both sides: \( 100 = x^2 - 44 \).

Step3: Solve for \( x \)

Add 44 to both sides: \( x^2 = 144 \). Take square roots: \( x = \pm 12 \).

Step4: Find \( y \) for \( x = 12 \)

Substitute \( x = 12 \) into \( y = 34x + 100 \): \( y = 34(12) + 100 = 408 + 100 = 508 \).

Step5: Find \( y \) for \( x = -12 \)

Substitute \( x = -12 \) into \( y = 34x + 100 \): \( y = 34(-12) + 100 = -408 + 100 = -308 \).

Answer:

\((12, 508)\), \((-12, -308)\)