6 6 systems of second degree equations
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This document discusses methods for solving systems of second-degree equations, including algebraic substitution or elimination methods and graphical methods. It provides 3 examples of solving systems of equations algebraically and graphically, including solving systems of quadratic equations and systems involving circles.
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1) Formulas are derived for tangent of the sum and difference of two angles using previous trigonometric identities: tan(留 + 硫) = (tan留 + tan硫) / (1 - tan留tan硫) and tan(留 - 硫) = (tan留 - tan硫) / (1 + tan留tan硫).
2) These formulas are valid when the tangents of the individual angles and their sum/difference are defined, which excludes cases where the cosine of any angle is 0.
3) Examples are provided to demonstrate applying these formulas to find the exact value of tangents of sums/differences of known angles.6.7 other methods for solving
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6 6 systems of second degree equations
- 1. 6-6 Systems of Second-Degree Equations Objective: Solve such systems algebraically and graphically.
- 2. 2 Methods 1. Algebraic Substitution or Elimination 2. Graphical
- 3. Example 1a: Solve the system xy = 6 and x2 + 4y2 = 64 algebraically.
- 5. Example 1b: Solve the system xy = 6 and x2 + 4y2 = 64 graphically.
- 6. Example 2: Find the points of intersection of two circles with equations x2 + y2 = 20 and (x 5)2 + (y 5)2 = 10.
- 8. Example 3: Solve the system 2x2 + y2 = 4 and x2 2y2 = 12.