Let x be the number of four credit courses and let y be the number of six credit courses.
We know that the student have completed 21 courses, this means that:
[tex]x+y=21[/tex]We also know that he has 104 credits in total. This means that:
[tex]4x+6y=104[/tex]Then we have the system of equations:
[tex]\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}[/tex]To solve the system we solve the first equation for y and plug the value in the second one. That is:
[tex]y=21-x[/tex][tex]\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}[/tex]Therefore, the student has taken 11 four credit courses.
