Question 160518
1.{{{-5x - 4y + 12z = -140}}}
2.{{{9x - 8y + z = -649}}}
3.{{{3x - 2y + 6z = -290 }}}

How about instead we get rid of y first. 
The z coefficients (-4,-8,-2) might be eaiser to start with.
Multiply eq. 1 by -2 and eq. 3 by -4 and add to eq. 2,
{{{9x-8y+z+(10x+8y-24z)=-649+280}}}
4.{{{19x-23z=-369}}}
{{{9x-8y+z+(-12x+8y-24z)=-649+1160}}}
5.{{{-3x-23z=511}}}
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Multiply eq. 5 by (-1) and add to eq. 4 to get rid of z.
{{{19x-23z+(3x+23z)=-369-511}}}
{{{22x=-880}}}
{{{highlight(x=-40)}}}
From eq. 4,
4.{{{19x-23z=-369}}}
{{{-760-23z=-369}}}
{{{-23z=391}}}
{{{highlight(z=-17)}}}
Finally, from eq. 1,
1.{{{-5x - 4y + 12z = -140}}}
{{{200-4y-204=-140}}}
{{{-4y=-136}}}
{{{highlight(y=34)}}}