Let x be the number of shirts and y be the number of pants, since the total number of articles must be 9, we can write
[tex]x+y=9\ldots(i)[/tex]Additionally, we know that the total cost must be $264 and 1 shirt cost $24 and 1 pant $36, then we can write
[tex]24x+36y=264\ldots(ii)[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} x+y=9 \\ 24x+36y=264 \end{gathered}[/tex]Solving by elimination method.
By multiplying the first equation by -24, we can obtain an equivalent system of equations:
[tex]\begin{gathered} -24x-24y=-216 \\ 24x+36y=264 \end{gathered}[/tex]Then, by adding both equations, we have
[tex]0+12y=48[/tex]Then, we get
[tex]\begin{gathered} 12y=48 \\ y=\frac{48}{12} \\ y=4 \end{gathered}[/tex]Now, in order to find x, we can substitute this result into equation (i). It yields,
[tex]x+4=9[/tex]which gives
[tex]\begin{gathered} x=9-4 \\ x=5 \end{gathered}[/tex]Therefore, the answer is 5 shirts and 4 pants.
