First, let's write it like this:
[tex]3a+2b=8[/tex]
Subtract [tex]2b[/tex] from both sides.
[tex]3a+2b-2b=8-2b[/tex]
[tex]3a=8-2b[/tex]
Divide both sides by 3.
[tex]\frac{3a}{3}=\frac{8-2b}{3}[/tex]
[tex]a=\frac{8-2b}{3}[/tex]
Now that we know what's the value of [tex]a[/tex], let's find the value of [tex]b[/tex]
[tex]3\cdot \frac{8-2b}{3}+2b=8[/tex]
Let's take the first part.
[tex]3\cdot \frac{8-2b}{3}[/tex]
Multiply the fractions.
[tex]=\frac{\left(8-2b\right)\cdot \:3}{3}[/tex]
Cancel the common factor, which is 3.
[tex]=8-2b[/tex]
We would be left with.
[tex]=8-2b+2b[/tex]
Add like terms.
[tex]=8[/tex]
We would be left with.
[tex]8=8[/tex]
Subtract 8 from both sides.
[tex]8-8=8-8[/tex]
[tex]0=0[/tex]
This tells us that [tex]b[/tex] can be any number.
Let me know if you need any help!
Thanks!
-TetraFish
