Question

solve the system of equations.
$y = x^{2} + 37x - 40$
$y = 37x + 24$
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 \( x^2 + 37x - 40 = 37x + 24 \).

Step2: Simplify equation

Subtract \( 37x + 24 \) from both sides: \( x^2 - 64 = 0 \).

Step3: Factor the equation

\( x^2 - 64 = (x - 8)(x + 8) = 0 \).

Step4: Solve for \( x \)

\( x - 8 = 0 \) or \( x + 8 = 0 \), so \( x = 8 \) or \( x = -8 \).

Step5: Find corresponding \( y \)

For \( x = 8 \), \( y = 37(8) + 24 = 320 \).
For \( x = -8 \), \( y = 37(-8) + 24 = -272 \).

Answer:

\((8, 320)\), \((-8, -272)\)