Question

solve the system of equations.
$y = x^2 + x - 49$
$y = x - 40$
write the coordinates in exact form. simplify all fractions and radicals.
( , )
( , )

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( x^2 + x - 49 = x - 40 \).

Step2: Simplify the equation

Subtract \( x \) and add 40 to both sides: \( x^2 - 9 = 0 \).

Step3: Factor the quadratic

\( (x - 3)(x + 3) = 0 \), so \( x = 3 \) or \( x = -3 \).

Step4: Find corresponding \( y \) values

For \( x = 3 \): \( y = 3 - 40 = -37 \).
For \( x = -3 \): \( y = -3 - 40 = -43 \).

Answer:

\((3, -37)\), \((-3, -43)\)