How do you solve the following linear system #5x + y+ 3z = - 7;- 4x + 4y - 2z= 22; 3x + y + 5z = 13#?

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Answer 1 · 2018-01-21T13:25:42

#x=-5#, #y=3# and #z=5#

From third equation, #y=13-3x-5z#

Hence, #5x+13-3x-5z+3z=-7# or #2x-2z=-20# and,

#-4x+4*(13-3x-5z)-2z=22# or #-16x-22z=-30#

From these equations,

#8*(2x-2z)-16x-22z=8*(-20)+(-30)#

#-16x-16z-16x-22z=-190#

#-38z=-190#, so #z=5#

Consequently,

#2x-2*5=-20#

#2x=-10#, so #x=-5#

Thus,

#y=13-3*(-5)-5*5=3#