Question 1124074
{{{system(x+y+z=10,2x+5y+6z=53,7x-y=4)}}}


What if first try to eliminate z?
{{{system(6x+6y+6z=60,2x+5y+6z=53)}}}

Subtract later from former.
{{{4x+y=7}}}


Revising the system now having just two variables,
{{{syste(4x+y=7,7x-y=4)}}}


Add the parts.
{{{11x+0=11}}}

{{{highlight(x=1)}}}


Using E3 of original system
{{{7x-4=y}}}
{{{7-4=y}}}
{{{highlight(y=3)}}}


Using E1 of original system
{{{1+3+z=10}}}
{{{highlight(z=6)}}}