54.6k views
0 votes
X+y-2z=-9
2x-y+8z=99
x-2y+5z=23
give the solution with z arbitrary

1 Answer

1 vote

Answer:

(x, y, z) = (-4, 29, 17)

Explanation:

These three equations have a unique solution. If you want "z arbitrary", you need to write a system of two equations with three variables (or, equivalently, a set of dependent equations).

It is convenient to let a graphing calculator, scientific calculator, or web site solve these.

_____

You can reduce the system to two equations in y and z by ...

subtracting the last equation from the first:

3y -7z = -32

subtracting twice the last equation from the second:

3y -2z = 53

Subtracting the first of these from the second, you get ...

5z = 85

z = 17

The remaining variable values fall out:

y = (53+2z)/3 = 87/3 = 29

x = -9 +2z -y = -9 +2(17) -29 = -4

These equations have the solution (x, y, z) = (-4, 29, 17).

User Sunriax
by
4.9k points