Solving a system of equations

[st3dent]

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!

[Bob3141592]

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 lets you define x_2 in terms of x_1 as a simple ratio. Eq 2 lets 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?

[jdavel]

st3dent,

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

[verty]

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.

[Dr Transport]

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.......

[st3dent]

Thank you.