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Section 6.1 Answers

  1. Consistent independent,
    Solution [latex]\left(6, -\frac{1}{2}\right)[/latex]
  2. Consistent independent,
    Solution [latex]\left(-\frac{7}{3}, -3\right)[/latex]
  3. Consistent independent,
    Solution [latex]\left(-\frac{16}{7}, -\frac{62}{7}\right)[/latex]
  4. Consistent independent,
    Solution [latex]\left(\frac{49}{12}, -\frac{25}{18}\right)[/latex]
  5. Consistent dependent,
    Solution [latex]\left(t, \frac{3}{2}t+3\right)[/latex] for all real numbers [latex]t[/latex]
  6. Consistent dependent,
    Solution [latex]\left(6-4t, t\right)[/latex] for all real numbers [latex]t[/latex]
  7. Inconsistent,
    No solution
  8. Inconsistent,
    No solution
  9. 13 chose the basic buffet and 14 chose the deluxe buffet.
  10. Mavis needs 20 pounds of \$3 per pound coffee and 30 pounds of \$8 per pound coffee.
  11. Skippy needs to invest \$6000 in the [latex]3\%[/latex] account and \$4000 in the [latex]8\%[/latex] account.
  12. 22.5 gallons of the [latex]10\%[/latex] solution and 52.5 gallons of pure water.

Section 6.2 Answers

  1. [latex](\pm 2, 0)[/latex], [latex]\left(\pm \sqrt{3}, -1\right)[/latex]
    The rectangular plane with the circle x squared plus y squared equals 4 and the parabola x squared minus y equals 4.
    Graphical Answer for Exercise 1
  2. No solution
    The rectangular plane with the circle x squared plus y squared equals 4 and the parabola x squared minus y equals 5.
    Graphical Answer for Exercise 2
  3. [latex](0, \pm 4)[/latex]
    The rectangular plane with the circle x squared plus y squared equals 16 and the ellipse 16 times x squared plus 4 times y squared equals 64.
    Graphical Answer for Exercise 3
  4. [latex](\pm 4,0)[/latex]
    The rectangular plane with the circle x squared plus y squared equals 16 and the hyperbola 9 times x squared minus 16 times y squared equals 144.
    Graphical Answer for Exercise 4
  5. [latex]\left(\pm \frac{4 \sqrt{7}}{5}, \pm \frac{12 \sqrt{2}}{5} \right)[/latex]
    The rectangular plane with the circle x squared plus y squared equals 16 and the hyperbola one ninth times x squared minus one sixteenth times y squared equals 1.
    Graphical Answer for Exercise 5
  6. [latex]\left( 1 + \sqrt{7}, -1 + \sqrt{7} \right)[/latex], [latex]\left( 1 - \sqrt{7}, -1 - \sqrt{7} \right)[/latex]
    The rectangular plane with the circle x squared plus y squared equals 16 and the line x minus y equals 2.
    Graphical Answer for Exercise 6
  7. [latex]\left( \pm \frac{2 \sqrt{10}}{5}, \pm \frac{\sqrt{15}}{5} \right)[/latex]
  8. [latex](0, 1)[/latex]
  9. [latex](0, \pm 1), \; (2, 0)[/latex]
  10. [latex]\left( \frac{4}{3}, \pm \frac{\sqrt{5}}{3} \right)[/latex]
  11. [latex](3, 4), \; (-4, -3)[/latex]
  12. [latex](\pm 3, 4)[/latex]
  13. [latex](-4, -56), \; (1, 9), \; (2, 16)[/latex]
  14. [latex](-2,2)[/latex], [latex](2,-2)[/latex]
  15. Initially, there are [latex]\frac{250000}{49} \approx 5102[/latex] bacteria. It will take [latex]\frac{5\ln(49/5)}{\ln(7/5)} \approx 33.92[/latex] minutes for the colony to grow to 50,000 bacteria.
  16. [latex]\left( -\sqrt[3]{5}, 49 \right)[/latex]
  17. .
    1. Answers May Vary
    2. Answers May Vary
    3. [latex]x^{4} + 4 = (x^{2} - 2x + 2)(x^{2} + 2x + 2)[/latex]

 

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