Can anyone show me how to get the answers to these four equations (show work please)?

Question

S1=10,000+5%S2+6.9%S3
S2=1,000+2.08%S1+3.45%S3
S3=26,090+7.29%S1+17.5%S2
S4=2,670+7.29%S1+2.5%S2+3.45%S3

Answer 1

S1 -.05S2 -.069S3 = - 10000 <-- Eq 1 rearranged
-.0208S1 +S2 - .0345S3 = 1000 <-- Eq2 rearranged
-.0729S1 -.175S2 +S3 = 26090 <-- Eq 3 rearranged
S4=2,670+.0729S1+.025S2+.0345S3 <-- Eq 4 rearranged
Eq1 , Eq2, and Eq3 are three equations in three unknowns which are S1,S2, and S3. So you must solve these three equations simultaneously to find the values of S1, S2 and S3. Then plug those values into Eq 4 and you will have S4.

You could start by multilying Eq 1 by .0208 and adding the result to Eq 2. This would give you a new Eq 5 where S1 has been eliminated.
Next eliminate S1 from Eq2 and Eq 3 getting Eq 6
Now you can solve Eq5 and Eq 6 for S2 and S3. This will then allow the computation of S3 and from there to S4.