Question 795381
Your first equation should be:
x + y = 26
The 2nd equation should be:
1x + 2y = 39

Now that we know the two equations we can use the addition/ elimination method to find our answer.
Let's use the first equation, since the coefficients are 1. 
We will multiply the first equation by -2 so the Y variable will cancel out.
-2(x + y = 26)
-2x - 2y = -52

Now that the Y variables are the same, we can add equation two and the new equation we made.
 -2x - 2y = -52 
+ 1x + 2y =  39
  -1x     =  -13
    x  =  13

Now that we have x we can plug in back into the original equations to find the value of the y variable. We will use the first equation since it is easier. 
x + y = 26
13 + y = 26
     y = 13

To check your work, plug x = 13 and y = 13 back into equations 1 and 2.
Equation 1
x + y = 26
13 + 13 = 26
26 = 26
Equation 2
1x +2y = 39
1(13) + 2(13) = 39
13 + 26 = 39
39 = 39

How many 1- credit courses are being taken? Thirteen 1- credit courses were taken
How many 2- credit courses are being taken? Thirteen 2- credit courses were taken