What is the solution of the quadratic system of equations? give brainliest and extra

(- 1, - 6 ) from the list

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

x² + 10x + 3 = - x² - 5 ( add x² - 5 to both sides )

2x² + 10x + 8 = 0 ( divide all terms by 2 )

x² + 5x + 4 = 0

(x + 1 )(x + 4 ) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into either of the 2 equations for y

x = - 1 : y = 1 - 10 + 3 = - 6 ( using y = x² + 10x + 3 )

x = - 4 : y = 16 - 40 + 3 = - 21

solutions are (- 1, - 6 ) or (- 4, - 21 )