Question

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

Answer 1

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)