How do you solve the system of equations algebraically #x+2y+3z=5, 3x+2y-2z=-13, 5x+3y-z=-11#?

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Answer 1 · 2016-12-30T16:50:29

The Soln. is #x=1,y=-4, &, z=4#.

Let us give nos. (1),(2) & (3) to the given eqns.

#3(3)+(1)rArr 15x+9y-3z+x+2y+3z=-33+5#

#rArr 16x+11y=-28.....................(4)#

#(2)-2(3)rArr 3x+2y-2z-10x-6y+2z=-13+22#

#rArr -7x-4y=9.......................(5)#

#4(4)+11(5) rArr 64x+44y-77x-44y=-112+99#

#rArr -13x=-13 rArr x=1..............(6)#

#(6) & (5) rArr -7-4y=9 rArr -4y=16#

# y=-4......................(7)#

#(6),(7) & (3) rArr 5-12-z=-11#

# z=4.................(8)#

Hence, the Soln. is #x=1,y=-4, &, z=4#.