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What are the solutions to the simultaneous equations of 3x -5y equals 16 and xy equals 7 shown by completing the square?
Wiki User
∙ 6y ago
If: 3x -5y = 16 then y = 0.6x -3.2
If: xy = 7 then x(0.6x -3.2) -7 = 0
Removing brackets: 0.6x^2 -3.2x -7 = 0
Dividing all terms by 0.6: x^2 -16/3x -35/3 = 0
Completing the square: (x -8/3)^2 -64/9 -35/3 = 0 => (x -8/3)^2 = 169/9
Square root both sides: x -8/3 = -13/3 or +13/3
Add 8/3 to both sides: x = -5/3 or x = 7
Solutions by substitution are: x = -5/3, y = -21/5 and x = 7, y = 1
Wiki User
∙ 6y ago
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