Dr. potter provides vaccinations against polio and measles. each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. last year, dr. potter gave a total of 60 vaccinations that consisted of a total of 184 doses. how many polio vaccinations and how many measles vaccinations did dr. potter give last year?

Let m be the amount is measles vaccines. and p be the amount of polio vaccines . 4p would be the amount of polio doses, and 2m would be the amount of measles doses. So the amount is measles an polio doses combined equals 2m + 4p.
2m + 4p = 184
Multiple by sides by half
1/2(2m + 4p) =1/2•184
Simplify
M+2p=92
Now comes he slightly more complicated part. In an equation, both sides are equal, so you can subtract the right side of an eqaution from the right side of a different eqaution and do the same thing with the left side.
M+p=60 because they are the number of vacaines. We can subtract this equation from other equation.

M+2p=92
M+p=60

M-m is 0, so it leaves. 2p-p is p, so the left side of our new equation is p. 92-60 is 32, so we end up with p=32. Then you can subtract p from p+m to get that m is 28.
Hope this helps.