Question

solve the system of equations.
$y = x^2 + 33x - 18$
$y = 36x - 14$
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 \( x^2 + 33x - 18 = 36x - 14 \).

Step2: Rearrange to quadratic

Subtract \( 36x \) and add \( 14 \): \( x^2 - 3x - 4 = 0 \).

Step3: Factor the quadratic

Find two numbers: \( -4 \) and \( 1 \), so \( (x - 4)(x + 1) = 0 \).

Step4: Solve for \( x \)

\( x - 4 = 0 \) or \( x + 1 = 0 \), so \( x = 4 \) or \( x = -1 \).

Step5: Find corresponding \( y \)

For \( x = 4 \): \( y = 36(4) - 14 = 124 \).
For \( x = -1 \): \( y = 36(-1) - 14 = -50 \).

Answer:

\((4, 124)\), \((-1, -50)\)