Stitz-Zeager_College_Algebra_e-book

Population when unchecked increases in a geometrical

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Unformatted text preview: x-axis of length 6 and a minor axis along the y -axis of length 4. We see from the graph that the two curves intersect at their y -intercepts only, (0, ±2). 2. We proceed as before to eliminate one of the variables (E 1) x2 + y 2 = 4 (E 2) 4x2 − 9y 2 = 36 Replace E 2 with −− − − −→ −−−−− −4E 1 + E 2 (E 1) x2 + y 2 = 4 (E 2) −13y 2 = 20 8.7 Systems of Non-Linear Equations and Inequalities 533 Since the equation −13y 2 = 20 admits no real solution, the system is inconsistent. To verify this graphically, we note that x2 + y 2 = 4 is the same circle as before, but when writing the 2 2 second equation in standard form, x − y4 = 1, we find a hyperbola centered at (0, 0) opening 9 to the left and right with a transverse axis of length 6 and a conjugate axis of length 4. We see that the circle and the hyperbola have no points in common. y y 1 −3 −2 −1 1 1 2 3 −3 x −2 −1 −1 x2 + y 2 = 4 4x2 + 9y 2 = 36 Graphs for 1 2 3 x −1 Graphs for x2 + y 2 = 4 4x2 − 9y 2 = 36 3. Since there are n...
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