Reducing a System of Equations to One Variable

st3dent
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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!
 
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st3dent said:
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!

Eq 3 let's you define x_2 in terms of x_1 as a simple ratio. Eq 2 let's you define a in terms ofx_1 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?
 
st3dent,

The cos(arcsin( )) in the solution that Bob3141592 showed you how to get can be simplified.
 
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.
 
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...
 
Thank you.
 

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