Homogeneous system of linear equations/Many variables/Two equations/1/Exercise

Solve the system of linear equations in the variables ${}x_{1},x_{2},\ldots ,x_{10}$, which is given by the two equations

${}x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+x_{7}+x_{8}+x_{9}+x_{10}=0\,$

and

${}x_{1}-x_{2}+x_{3}-x_{4}+x_{5}-x_{6}+x_{7}-x_{8}+x_{9}-x_{10}=0\,.$

Create a solution