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Question 45685: solve the system
4x+y=-5
4x-z=3
y+z=-8
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 4x+y=-5 ......I
4x-z=3 ........II
y+z=-8 .........III
EQN.I-EQN.II
Y+Z=-5-3=-8........IV
EQN.III-EQN.IV
0=-8+8=0......THE EQNS ARE DEPENDENT AND CONSISTENT..HENCE INFINITE SOLUTIONS
GIVE ANY VALUE TO Y SAY 0
Z=-8-0=-8
4X=-5
X=-5/4
HENCE X=-5/4,Y=0,Z=-8 IS A SOLUTION SET
IN GENERAL GIVING ANY VALUE TO Y THE SOLUTION SET IS
Y=Y ANY VALUE
Z=-8-Y
X=(-5-Y)/4...IS A SOLUTION SET
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