Given The System Of Equations

Question

Given the system of equations:

x+y+z=−5

y−3z=5

2x+y+5z=−14

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(I don't know how to create the bracket for the above)

(a) Determine the type of system: inconsistent or dependent

(b) If your answer is dependent, find the complete solution.

Write x, y, and z as functions of t, where z=t.

Answer 1

The system is inconsistent....

Eliminates x....

-2 * equation 1 + equation 3:

-y + 3z = -4

2 by 2 system:

y - 3z = 5

-y + 3z = -4

Adding them together:

0 = 1

which is inconsistent.

there is no solution

So as to further verify, by substitution,

y = 3z+5

substitutes into equations 1 and 3:

x + 3z+5 + z = -5

x + 4z + 5 = -5

x + 4z = -10

AND

2x + 3z+5 + 5z = -14

2x + 8z + 5 = -14

2x + 8z = -19

2 by 2 system:

x+ 4z = -10

2x + 8z = -19

then x = -10-4z

2(-10-4z) + 8z = -19

-20 - 8z + 8z = -19

-20 = -19

Definitely inconsistent.

No solution