Algebra

Matrices & Determinants

Medium

applied

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

$x = 0.5$ , $y = 1.5$ , $z = 1.5$

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

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

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

✅ Correct Option: 4

The system of equations:

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

$2y = 3$

$x + 2z = 4$

From the second equation:

$2y = 3$

$y = \frac{3}{2} = 1.5$

From the third equation:

$x + 2z = 4$

$x = 4 - 2z$

Substitute $x = 4 - 2z$ and $y = 1.5$ into the first equation:

$2(4 - 2z) + \frac{1}{2}(1.5) - z = 1$

$8 - 4z + 0.75 - z = 1$

$8.75 - 5z = 1$

$-5z = -7.75$

$z = 1.55$

Substitute $z = 1.55$ into $x = 4 - 2z$ :

$x = 4 - 2(1.55)$

$x = 4 - 3.1$

$x = 0.9$

Therefore, the solution is $x = 0.9$ , $y = 1.5$ , $z = 1.55$

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