Question

1. solve the system of equations. write your answer(s) as ordered pair(s)\\( y = 4x^2 - 17x + 1 \\)\\( y = 3x - 15 \\)

Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( 4x^2 - 17x + 1 = 3x - 15 \).
\( 4x^2 - 17x + 1 - 3x + 15 = 0 \)

Step2: Simplify quadratic

Combine like terms: \( 4x^2 - 20x + 16 = 0 \).
Divide by 4: \( x^2 - 5x + 4 = 0 \).

Step3: Factor quadratic

Factor: \( (x - 1)(x - 4) = 0 \).

Step4: Solve for \( x \)

Set each factor to 0: \( x - 1 = 0 \) or \( x - 4 = 0 \), so \( x = 1 \) or \( x = 4 \).

Step5: Find corresponding \( y \)

For \( x = 1 \): \( y = 3(1) - 15 = -12 \).
For \( x = 4 \): \( y = 3(4) - 15 = -3 \).

Answer:

\((1, -12)\), \((4, -3)\)