Question

solve the system of equations.
$y = 10x + 45$
$y = x^2 + 10x + 9$
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 \( 10x + 45 = x^2 + 10x + 9 \).

Step2: Simplify equation

Subtract \( 10x + 45 \) from both sides: \( 0 = x^2 - 36 \).

Step3: Solve for \( x \)

Factor: \( x^2 - 36 = (x - 6)(x + 6) = 0 \), so \( x = 6 \) or \( x = -6 \).

Step4: Find \( y \) for \( x = 6 \)

Substitute \( x = 6 \) into \( y = 10x + 45 \): \( y = 10(6) + 45 = 105 \).

Step5: Find \( y \) for \( x = -6 \)

Substitute \( x = -6 \) into \( y = 10x + 45 \): \( y = 10(-6) + 45 = -15 \).

Answer:

\((6, 105)\)
\((-6, -15)\)