Question 849834
1.{{{3x+5y-2z=7}}}
2.{{{5x+4y+5z=-13}}}
3.{{{3x-2y+4z=-3}}}
Subtract eq. 3 from eq. 1,
{{{3x+5y-2z-3x+2y-4z=7+3}}}
4.{{{7y-6z=10}}}
Multiply eq. 1 by 5 and eq. 2 by -3 and add them,
{{{15x+25y-10z-15x-12y-15z=35+39}}}
5.{{{13y-25z=74}}}
Now x is elmininated.
Multiply eq. 4 by 13 and eq. 5 by (-7) and add them,
{{{91y-78z-91y+175z=130-518}}}
{{{97z=-388}}}
{{{z=-4}}}
Now back substitute to find {{{y}}}
{{{7y-6(-4)=10}}}
{{{7y=-14}}}
{{{y=-2}}}
and finally,
{{{3x+5(-2)-2(-4)=7}}}
{{{3x-10+8=7}}}
{{{3x=9}}}
{{{x=3}}}