3. Five mark example problems - I

1. Solve the following system of linear equations in three variables.

 

\(3x - 2y + z = 2\), \(2x + 3y - z = 5\), \(x + y + z = 6\).

 

Answer:

 

\(x =\)

 

\(y =\)

 

\(z =\)

 

2. In an interschool athletic meet, with a total of \(24\) individual prizes, securing a total of \(56\) points, a first place secures \(5\) points, a second place secures \(3\) points, and a third place secures \(1\) point. Having as many third-place finishers as first and second-place finishers, find how many athletes finished in each place.

 

Answer:

 

The number of first place finishers is .