4. Five mark example problems - II

1. Solve \(3x + y - 3z = 1\); \(-2x - y + 2z = 1\); \(-x - y + z = 2\).

 

Answer:

 

The system has no solutioninfinitely many solutionsa unique solution.

 

2. Solve \(\frac{x}{2} - 1 = \frac{y}{6} + 1 = \frac{z}{7} + 2\); \(\frac{y}{3} + \frac{z}{2} = 13\)

 

Answer:

 

\(x =\)

 

\(y =\)

 

\(z =\)

 

3. Solve \(\frac{1}{2x} + \frac{1}{4y} - \frac{1}{3z} = \frac{1}{4}\); \(\frac{1}{x} = \frac{1}{3y}\); \(\frac{1}{x} - \frac{1}{5y} + \frac{4}{z} = 2 \frac{2}{15}\)

 

Answer:

 

\(x =\)

 

\(y =\)

 

\(z =\)