Let x be number of multiple-choice questions and y be number of short answer questions. Total number of questions are 15, so
[tex]\begin{gathered} x+y=15 \\ y=15-x \end{gathered}[/tex]The worth of multiple choice question is 2 points, so worth of x multiple choice questions are 2x and worth of y short answer questions are 5y. Total worth of test is 60. So equation is,
[tex]2x+5y=60[/tex]