Given a system of equations are
[tex]5x-2y+3z=6\text{ take it as equation (1)}[/tex][tex]2x-4y-3z=14\text{ take it as equation (2)}[/tex][tex]x+6y-8x=12\text{ take it as equaiton (3)}[/tex]Adding equation (1) and equation (2), we get
[tex](5x-2y+3z)+(2x-4y-3z)=6+14[/tex][tex]5x+2x_{}-2y-4y+3z-3z=20[/tex][tex]7x_{}-6y=20\text{ take it as equation (4)}[/tex]Multiplying equation (2) by 8, we get
[tex]8\times2x-8\times4y-8\times3z=8\times14[/tex][tex]16x-32y-24z=112\text{ take it as equation (5)}[/tex]Multiplying equation (3) by (-3), we get
[tex](-3)x+(-3)6y-(-3)8x=(-3)12\text{ }[/tex][tex]3x-18y+24x=-36\text{ take it as equation (6)}[/tex]Adding equation (5) and equation (6), we get
[tex](16x-32y-24z)+(3x-18y+24x)=112-36[/tex][tex]16x+3x-32y-18y-24z+24x=76[/tex][tex]19x-50y=76[/tex]Adding 50 on both sides, we get
[tex]19x-50y+50y=76+50y[/tex][tex]19x=76+50y[/tex]Dividing by 19. we get
[tex]x=\frac{76+50y}{19}[/tex][tex]\text{ Substitute }x=\frac{76+50y}{19}\text{ in equation (4) as follows}[/tex][tex]7(\frac{76+50y}{19}_{})-6y=20\text{ }[/tex][tex](\frac{7\times76+7\times50y}{19}_{})-\frac{19\times6y}{19}=20\text{ }[/tex][tex]\frac{532+350y-114y}{19}=20\text{ }[/tex][tex]532+236y=20\times19[/tex][tex]236y=380-532[/tex][tex]y=-\frac{152}{236}[/tex][tex]y=-0.644[/tex][tex]\text{ Substitute y=-0.644 in equation }x=\frac{76+50y}{19}\text{as follows}[/tex][tex]\text{x}=\frac{76+50(-0.644)}{19}[/tex][tex]x=2.301[/tex]Substitute x=2.301 and y=-0.644 in equation (1), we get
[tex]5(2.301)-2(-0.644)+3z=6[/tex][tex]12.838+3z=6[/tex][tex]z=\frac{6-12.828}{3}[/tex][tex]z=-2.279[/tex]Hence the solutions are
[tex]x=2.301[/tex][tex]y=-0.644[/tex][tex]z=-2.279[/tex]