How do you solve 4x + 5y - 2z = 23, -6x + 2y + 7z = -14, and 8x + 3y + 3z = 11?

1 Answer
May 1, 2018

Answer:

#x=1, y=3, z=-2#

Explanation:

#4x+5y-2z=23=># eq-1
#-6x+2y+7z=-14=># eq-2
#8x+3y+3z=11=># eq-3

Eliminate #Z# between 1 & 2: multiply by 7 & 2 respectively, then add the equations:

#28x+35y-14z=161#
#-12x+4y+14z=-28#
#16x+39y=133=># eq-4

Eliminate #Z# between 2 & 3: multiply by 3 & -7 respectively, then add the equations:

#-18x+6y+21z=-42#
#-56x-21y-21z=-77#
#-74x-15y=-119=># eq-5

Eliminate #y# between 4 & 5: multiply by 15 & 39 respectively, then add the equations, #y's# cancel, solve for #x#:

#240x+585y=1995#
#-2886x-585y=-4641#
#-2646x=-2646#
#x=1=># plug in eq-4 solve for #y#:
#39y=117#
#y=3=># plug in for x & y in eq-1 solve for #z#:
#4+15-2z=23#
#-2z=4#
#z=-2#