Question

Solve the system, if possible. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter a general solution in terms of x, y, or z.)


x + y + z = 7
2x + y + z = 14
x + 2y + 3z = 2

Answer 1

none of those lines is parallel, so I should be able to find a solution.

first work on the first two by elimination

x + y + z = 7
2x + y + z = 14
---------------- subtract
- x + 0 + 0 = -7
so
x = 7
well that gives us a running start
7 + y + z = 7
14 + y + z = 14
both yield
y + z = 0 so z = -y
now the last equation with x = 7 and z = -y
7 + 2 y + 3(-y) = 2
-y = -5
so
y = 5
and
z = -y = -5