Question

Solve the simultaneous equation

Answer 1

First of all, we can simply the first and second equations by $2$ and $3$, respectively, to get

$x+y+2z=12$

$2x+y=5$

$y+2z=11$

If we subtract the third equation from the first, we already figure out that $x=1$. The system becomes

$y+2z=11$

$y=3$

$y+2z=11$

so we know $y=3$ as well. Let's plug the values for $x$ and $y$ in any of the three equations to get

$y+2z=11 \iff 3+2z=11 \iff 2z=8 \iff z=4$

So, the solution is $x=1$, $y=3$, $z=4$