The solution of the system of equations $2x +\frac{1}{2}y-z=1,2y= 3, x+2z = 4$ is:

$x= 0.9, y = 1.5, z = 1.55$

The correct answer is Option (4) → $x= 0.9, y = 1.5, z = 1.55$

Given system:

$2x + \frac{1}{2}y - z = 1$

$2y = 3$

$x + 2z = 4$

From $2y = 3$:

$y = \frac{3}{2}$

Use $x + 2z = 4$ → $x = 4 - 2z$

Substitute into first equation:

$2(4 - 2z) + \frac{1}{2}\left(\frac{3}{2}\right) - z = 1$

$8 - 4z + \frac{3}{4} - z = 1$

$8.75 - 5z = 1$

$-5z = -7.75$

$z = \frac{7.75}{5} = \frac{31}{20}$

Now compute $x$:

$x = 4 - 2\left(\frac{31}{20}\right)$

$x = 4 - \frac{62}{20}$

$x = \frac{80}{20} - \frac{62}{20}$

$x = \frac{18}{20} = \frac{9}{10}$

The solution is: $x = \frac{9}{10},\; y = \frac{3}{2},\; z = \frac{31}{20}$.