x - y = 6, xy = 4

Question

solve the simultaneous equation give d answers in thir simplest from..plssss help me really need the help

Answer 1

x - y = 6; this is a line through (0,-6) and (6,0).

xy = 4
y = 4/x; this is a hyperbola in Quadrants I and III

So line will intersect hyperbola in Quadrants I and III
=> solution points will be of the form (-,-) & (+,+)

x - 4/x = 6

Multiply both sides by x:

x^2 - 4 = 6x

x^2 - 6x - 4 = 0
a = 1, b = -6, c = -4

x = (-b ± √(b^2 - 4ac))/(2a)

b^2 - 4ac = (-6)^2 - 4(1)(-4) = 4(9) + 4(4) = 4(13)
=> 2 real irrational roots

x = (-(-6) ± √(4(13)))/(2(1)) = (6 ± 2√(13))/2

x = 3 ± √(13)

y = 4/x = 4/(3 ± √(13))

y = 4(-3 ± √(13))/((-3 ± √(13))(3 ± √(13)))

y = 4(-3 ± √(13))/(-9 + 13)

y = -3 ± √(13)

Solution points are:
(3 - √(13),-(3 + √(13))), and
(3 + √(13),-(3 - √(13)));

which are of the form (-,-) and (+,+).

Here’s a GeoGebra graph:
http://www.wyzant.com/resources/files/262611/line_hyperbola