9514 1404 393
Answer:
(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.
