Question 222888: find all of the ordered pairs, (x,y) of integers that satisfy all four of the given equations: 5*x*3*y=180, x^2+y^2=40, 8*x-8*y=32, 12x/4y=1 The ordered pair has to satisfy all equations and i have to find all of them. for example, if x=5 and y=9, that ordered pair needs to work for every equation. I'm guessing since it says find all of them, there is probably more than one.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I think they gave your 4 equations just to scare you a bit. It turns out that the four equations  ,  ,  , and  are a hyperbola, a circle, and two straight lines respectively. Since and are equations of lines, you need to satisfy all 4 equations, and the intersection of two lines is either going to give you a) no solutions, b) infinite solutions, or c) 1 solution, this means that your best bet is to solve the system 
Note: you should find that there is only one solution to the system of two equations above, which would mean that there is only one solution to the given system of four equations.
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