How do you solve the system #x+y-z=2#, #3x+5y-2z=-5#, and #5x+4y-7z=-7#?

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Answer 1 · 2016-09-05T05:46:49

The soln. : #x=30, y=-13, z=15#.

Let us solve the system of eqns. using Elimination Method.

From the First eqn., #z=x+y-2#

Using this #z# in the second and the third eqns., we get,

#3x+5y-2(x+y-2)=-5", i.e., "x+3y=-9#

#5x+4y-7(x+y-2)=-7", or, "-2x-3y=-21#

Adding these last eqns., #x=30#.

Then from, #x+3y=-9, y=-13#.

Finally, #z=x+y-2=15#.

These roots satisfy the given eqns.

The soln. : #x=30, y=-13, z=15#.