SOLUTION: 3b+2a=2 and -2b+a=8

Algebra ->  Expressions-with-variables -> SOLUTION: 3b+2a=2 and -2b+a=8      Log On


   

Question 132472This question is from textbook Algebra 1
: 3b+2a=2 and -2b+a=8 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

system%283b%2B2a=2%2C-2b%2Ba=8%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for a.




So let's isolate a in the first equation

3b%2B2a=2 Start with the first equation


2a=2-3b Subtract 3b from both sides


2a=-3b%2B2 Rearrange the equation


a=%28-3b%2B2%29%2F%282%29 Divide both sides by 2


a=%28%28-3%29%2F%282%29%29b%2B%282%29%2F%282%29 Break up the fraction


a=%28-3%2F2%29b%2B1 Reduce



---------------------

Since a=%28-3%2F2%29b%2B1, we can now replace each a in the second equation with %28-3%2F2%29b%2B1 to solve for b



-2b%2Bhighlight%28%28%28-3%2F2%29b%2B1%29%29=8 Plug in a=%28-3%2F2%29b%2B1 into the first equation. In other words, replace each a with %28-3%2F2%29b%2B1. Notice we've eliminated the a variables. So we now have a simple equation with one unknown.



%282%29%28-2b-%283%2F2%29b%2B1%29=%282%29%288%29 Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-4b-3b%2B2=16 Distribute and multiply the LCM to each side



-7b%2B2=16 Combine like terms on the left side


-7b=16-2Subtract 2 from both sides


-7b=14 Combine like terms on the right side


b=%2814%29%2F%28-7%29 Divide both sides by -7 to isolate b



b=-2 Divide





-----------------First Answer------------------------------


So the first part of our answer is: b=-2









Since we know that b=-2 we can plug it into the equation a=%28-3%2F2%29b%2B1 (remember we previously solved for a in the first equation).



a=%28-3%2F2%29b%2B1 Start with the equation where a was previously isolated.


a=%28-3%2F2%29%28-2%29%2B1 Plug in b=-2


a=6%2F2%2B1 Multiply


a=4 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is: a=4









-----------------Summary------------------------------

So our answers are:

b=-2 and a=4