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X-y equals 5 and x squared-y squared equals 5 How do you work this out using simultaneous equations?
Wiki User
∙ 14y ago
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Gaston Adams
Wiki User
∙ 14y agox - y = 5
x^2 - y^2 = 5
Subtract the first equation from the second equation.
x^2 - y^2 - x - (-y) = 5 - 5
(x^2 - y^2) - (x - y) = 0
(x - y)(x + y) - (x - y) = 0
(x - y)(x + y - 1) = 0
x - y = 0 or x + y - 1 = 0
x = y do not satisfy both equations of the system, so x cannot be equal to y. Thus we need to find the values of x and y for which x + y - 1 = 0 is true.
x + y - 1 = 0
x = 1 - y
Substitute 1 - y for x to x - y = 5.
x - y = 5
1 - y - y = 5
- 2y = 4
y = -2
Substitute -2 for y to x = 1 - y
x = 1 - y
x = 1 -(-2)
x = 3
Thus the solution of the system is (3, -2).
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