# How do you solve using gaussian elimination or gauss-jordan elimination, 3x + y - 3z =3, x + 3y - z = -7, 3x + 3y - z = -1?

Dec 13, 2017

$x = 3$, $y = - 3$ and $z = 1$

#### Explanation:

From second equation, $z = x + 3 y + 7$

I took value of $z$ into third one,

$3 x + 3 y - \left(x + 3 y + 7\right) = - 1$

$2 x - 7 = - 1$

$2 x = 6$, so $x = 3$

After taking value of $z$ into first one,

$3 x + y - 3 \cdot \left(x + 3 y + 7\right) = 3$

$- 8 y - 21 = 3$

$- 8 y = 24$, so $y = - 3$

Thus $z = x + 3 y + 7 = 3 + 3 \cdot \left(- 3\right) + 7 = 3 - 9 + 7 = 1$