What is one of the solutions to the following systems of equations? Y squared plus X squared equals 65 and Y plus X equals seven

Step-by-step explanation:

y^2 + x^2 = 65

y + x = 7 ... x = 7 - y

y^2 + (7 - y) ^2 = 65

y^2 + (7 - y) (7 - y) = 65

y^2 + 49 - 7y - 7y + y^2 = 65

2y^2 - 14y + 49 = 65

2y^2 - 14y + 49 - 65 = 0

2y^2 - 14y - 16 = 0

2 (y^2 - 7y - 8) = 0

2 (y + 1) (y - 8) = 0

y + 1 = 0 y - 8 = 0

y = - 1 y = 8

solution:

y = - 1 ... y + x = 7 ... - 1 + x = 7 ... x = 7 + 1 ... x = 8 ... (8,-1)

y = 8 ... y + x = 7 ... 8 + x = 7 ... x = 7 - 8 ... x = - 1 ... (-1,8)