Question 253952
We have three equations:
(i) {{{x+y-2z=0}}}
(ii) {{{3x+y=1}}}
(iii) {{{5x+3y+7z=2}}} 
solve (ii) for y. We get
(iv) {{{y = -3x + 1}}}
substitute (iv) into (i) and (iii) to get 2 equations with two variables.
(v) {{{x+(-3x+1)-2z=0}}}
(vi) {{{5x+3(-3x+1)+7z=2}}}
simplify (v) and (vi) to get
(vii) {{{-2x-2z=-1}}
(viii) {{{-4x+7z=-1}}}
multiply (vii) by -2 to get
(ix) {{{4x + 4z = 2}}}
(viii) {{{-4x + 7z = -1}}}
add down to eliminate x and solve for z. We get
(x) 11z = 1 - -> z = 1/11.
Find x.
x = 9/11
Find y.
y = -16/22
So, we have
{9/22 , -5/22 , 1/11}