Question

What is the solution of quadratic system of equations ?

Answer 1

Answer:

(- 1, 1) and (- 5, - 35)

Step-by-step explanation:

since both equations express y in terms of x, equate the right sides

x² + 15x + 15 = - x² + 3x + 5 ( subtract - x² + 3x + 5 from both sides )

2x² + 12x + 10 = 0  ( divide all terms by 2 )

x² + 6x + 5 = 0 ← in standard form

(x + 1)(x + 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 5 = 0 ⇒ x = - 5

substitute these values into either of the 2 equations and solve for y

x = - 1 : y = (- 1)² + 15(- 1) + 15 = 1 - 15 + 15 = 1 ⇒ (- 1, 1 )

x = - 5 : y = (- 5)² + 15(- 5) + 15 = 25 - 75 + 15 = - 35 ⇒ (- 5, - 35 )

None of the given options