unit rate in systems of equations

1. 

12o+7a=5.36

 8o+5a=3.65 

Multiply the first equation through by 5    and the second through by -7

So we have

60o  + 35a   =  26.8

-56o -  35a  =  - 25.55          add these

4o   =  1.25  =  5/4    divide both sides by  4

o =  5/16  =  .3125

We can find a with any of the equations

8(5/16) + 5a  =  3.65

5/2 +  5a  = 3.65

2.5  + 5a  = 3.65      subtract  2.5 from each side

5a  =  1.15       divide both sides by 5

a  =  .23

So... {o, a}    =   { .3125, .23 }

2.

4p+5c=6.71

5p+3c=7.12

Multiply the first equation by 3    and the second by - 5

12p  + 15c   =  20.13

-25p  - 5c   =  -35.60            add these

-13p   =  -15.47      divide both sides by -13

p  =  1.19

Using  any equation to find c, we have

4(1.19)  + 5c  = 6.71  

4.76  + 5c  = 6.71     subtract 4.76 from both sides

5c  = 1.95     divide both sides by 5

c  = 0.39

So   .... { p, c }  =  { 1.19, 0.39}