SOLUTION: 5a+24b=109.60 16a+24b=171 Have got this far. I understand how to write it in elimination. Please show me how to write it correctly in substitution form

Algebra ->  Expressions-with-variables -> SOLUTION: 5a+24b=109.60 16a+24b=171 Have got this far. I understand how to write it in elimination. Please show me how to write it correctly in substitution form      Log On


   

Question 146071: 5a+24b=109.60
16a+24b=171
Have got this far. I understand how to write it in elimination.
Please show me how to write it correctly in substitution form
Found 2 solutions by checkley77, edjones:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
5a+24b=109.60
5a=109.6-24b
a=109.6/5-24b/5
now substitute (109.6/5-24b/5) for a in the other equation & solve for b.
16a+24b=171
16(109.6/5-24b/5)+24b=171
1753.6/5-384b/5+24b=171
-384b/5+24b=171-1753.6/5
(-384b+5*24b)/5=(5*171-1753.6)/5
(-384b+120b)/5=(855-1753.6)/5
264b/5=898.6/5 csncelling out the denominators we have:
264b=898.6
b=989.6/264 answer.
16a+24(898.6/264)=171
16a+21566.4/264=171
16a=171-21566.4/264
16a=(171*264-21566.4)/264
16a=(45144-21566.4)/264
16a=23577.6/264
a=(23577.6/264)(1/16)
a=23577.6/4224
a=61.4/11 answer.


Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5a+24b=109.60
16a+24b=171
.
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 24*b to the right, we get:
5%2Aa+=+109.6+-+24%2Ab, or a+=+109.6%2F5+-+24%2Ab%2F5. Substitute that
into another equation:
16%2A%28109.6%2F5+-+24%2Ab%2F5%29+%2B+24%5Cb+=+171 and simplify: So, we know that b=3.40378787878788. Since a+=+109.6%2F5+-+24%2Ab%2F5, a=5.58181818181817.

Answer: system%28+a=5.58181818181817%2C+b=3.40378787878788+%29.