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Solving a system of equations

  1. Apr 11, 2004 #1
    Hello, I am difficulty solving this system of equations.

    Eqn1: 1.0416*10-21 = 4.75*10-27(x2) + 1.68*10-27(x1)(cos a)

    Eqn2: 2.827 = (x1)(sin a)

    Eqn3: 3.22896*10-16 = 8.4*10-28(x2)2 + 3.36*10-27(x1)2

    I keep on getting equations with two variables in it. Can someone tell me how to get an eqn with only one variable out of this system.. Thanks!
  2. jcsd
  3. Apr 11, 2004 #2
    Eq 3 lets you define [itex]x_2[/itex] in terms of [itex]x_1[/itex] as a simple ratio. Eq 2 lets you define a in terms of[itex]x_1[/itex] using an arcsin. Substituting these into Eq 1 will give you an equation with only one variable, although it will contain the cos of an arcsin.

    Does that help?
  4. Apr 11, 2004 #3

    The cos(arcsin( )) in the solution that Bob3141592 showed you how to get can be simplified.
  5. Apr 12, 2004 #4


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    Eq 2 gives you 'x_1 = 2.827/sin(a)'. Substitute this for x_1 in Eq 1 and 3, then in each solve for x_2 and equate. Can then calc 'a' and work back.
  6. Apr 12, 2004 #5

    Dr Transport

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    solve the first equation for x_1 cos(a), square, then add to the second equation squared. Substitute into the third equation for x_1^2, you only have one unknown then.........backsubstitute.......
  7. Apr 12, 2004 #6
    Thank you.
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