Find all solutions to the following system of equations. x = 1.5x(1 − x) − 0.6xy
y = y + 2xy − 0.5y
(x, y) = (
Incorrect: Your answer is incorrect.
(smallest x-value)
(x, y) =
Incorrect: Your answer is incorrect.

(x, y) =
Incorrect: Your answer is incorrect.
(largest x-value)

9514 1404 393

  (x, y) = (0, 0), (1/3, 0), (1/4, 5/24)

Step-by-step explanation:

It is often helpful to write equations in general form. That way, factoring and use of the zero product rule can find solutions.

  x = 1.5x(1 -x) -0.6xy . . . . given

  1.5x -1.5x² -0.6xy -x = 0 . . . . . subtract x

  0.5x -1.5x² -0.6xy = 0 . . . . . . . collect terms

  0.1x(5 -15x -6y) = 0 . . . . . . . . factor; [eq1]

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  y = y +2xy -0.5y . . . . . . given

  y +2xy -0.5y -y = 0 . . . . . subtract y

  -0.5y +2xy = 0 . . . . . . . . . . collect terms

  -0.5y(1 -4x) = 0 . . . . . . . factor; [eq2]

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Solutions to [eq1] will be ...

  x = 0

  15x +6y = 5 . . . . . . a set of possible solutions

Solutions to [eq2] will be ...

  y = 0

  1 -4x = 0   ⇒   x = 1/4

Then (x, y) pairs that will satisfy both equations simultaneously are ...

  (x, y) = (0, 0), (1/3, 0), (1/4, 5/24)

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In the attached graph, solutions to [eq1] are the red lines; solutions to [eq2] are the green lines. Then simultaneous solutions to both equations are found at the intersection points of red and green lines.

answer: approximately 206 bones

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