[ $\underline{\text { Systems of linear equations }}$]

Solve the system of equations

$5732 x+2134 y+2134 z=7866$,

$2134 x+5732 y+2134 z=670$

$2134 x+2134 y+5732 z=11464$.
Solve all the equations.

## Solution

By adding the equations, we get $x+y+z=2$ or $2134(x+y+z)=4268$. Subtracting the obtained combination from each equation, we get the values of all variables.

## Answer

$(1,-1,2)$.

Solve the system of equations

$x+y+u=4$

$y+u+v=-5$,

$u+v+x=0$,

$v+x+y=-8$.

## Hint

Add all the equations.

## Solution

By adding all the equations, we get $3(x+y+u+v)=-9$, or $x+y+u+v=-3$. Therefore, $x=(x+y+u+v)-(y+u+v)=-3-(-5)=2$. Similarly, we find the other unknowns.

## Answer

$(2,-3,5,-7)$.