(- 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 )
