Answer:
[tex]x=21\\y=-17\\z=0[/tex]
Step-by-step explanation:
Multiply the second equation by -1:
[tex](-1)5x+6y+5z=3(-1)\\-5x-6y-5z=-3[/tex]
Add this equation and the third equation and solve for "z":
[tex]\left \{ {{-5x-6y-5z=-3} \atop {5x+6y+3z=3}} \right.\\.........................\\-2z=0\\z=0[/tex]
Substitute [tex]z=0[/tex] into two original equations:
[tex]2x+2y+6(0)=8[/tex]
[tex]2x+2y=8[/tex] [Equation A]
[tex]5x+6y+5(0)=3[/tex]
[tex]5x+6y=3[/tex] [Equation B]
Multiply the Equation A by -3, add both equations and then solve for "x":
[tex]\left \{ {{-6x-6y=-24} \atop {5x+6y=3}} \right.\\.....................\\-x=-21\\x=21[/tex]
Substitute [tex]x=21[/tex] into the Equation A or the Equation B and solve for "y":
[tex]2(21)+2y=8\\\\42+2y=8\\\\2y=8-42\\\\2y=-34\\\\y=\frac{-34}{2}\\\\y=-17[/tex]
