Question 8017
Since there are two numbers that are represented by "unknowns" (C and a) you can try to find out what C is and then use it to find a.
The first equation says
{{{a/2 + C = 19}}} 
{{{a/2 = 19 - C}}} [subtracting C from both sides]
{{{a/2 - 19 = -C}}} [subtracting 19 from both sides]
{{{C = 19 - a/2}}} [multiplying both sides by -1 and rearranging]
This value for C can be put into the second equation
{{{a/4 - 3C = -8}}}
{{{a/4 -3(19 - a/2) = -8}}} [putting 19-a/2 for C]
{{{a/4 - 57 + 3a/2 = -8}}} [multiplying each term in the group by -3]
{{{a/4 - 57 + 6a/4 = -8}}} [getting a common denominator of 4 for the fractions]
{{{7a/4 - 57 = -8}}} [adding the fractions]
{{{7a/4 = 49}}} [adding 57 to both sides]
{{{7a = 196}}} [multiplying both sides by 4]
{{{a = 28}}} [dividing both sides by 7]
Now put the value for a in the equation for C
{{{C = 19 - 28/2 = 19 - 14 = 5}}}
Checking:
28/2 + 5 = 14 + 5 = 9
28/4 - 15 = 7 - 15 = -8