Answer :
Let D be the CDs and C for the cassetes. We can write the first statement as
[tex]2D+3C=75[/tex]and the second statement as
[tex]1D+5C=76[/tex]Then, we must solve these equations.
Solving by elimination method.
We can multiply by -2 the second equation. Then, we have the following system of equations:
[tex]\begin{gathered} 2D+3C=75 \\ -2D-10C=-152 \end{gathered}[/tex]We can see that if we add both equations, we obtain
[tex]3C-10C=75-152[/tex]because 2D-2D=0. Then, we have
[tex]-7C=-77[/tex]If we move the coefficient -7 of C to the right hand side, we have
[tex]\begin{gathered} C=\frac{-77}{-7} \\ C=11 \end{gathered}[/tex]Now, we can substitute this value into the first equation in order to find D. It yields,
[tex]\begin{gathered} 2D+3(11)=75 \\ 2D+33=75 \\ 2D=75-33 \\ 2D=42 \\ D=\frac{42}{2} \\ D=21 \end{gathered}[/tex]Then, the answer is C=11 and D=21. So, the cost for the CDS is $21 and for the cassettes is $11.