Question 192037
Solve the system, if possible
x - 4y + z= 9
3y -2z= -7
-x +z= 0 
;
let's rewrite it and add:
x - 4y + z = 9
0x +3y -2z = -7
-x +0y + z = 0
----------------Addition eliminates x and z
-y = 2
y = -2
:
Find z using the 2nd original equation
3(-2) - 2z = -7
-6 - 2z = -7
-2z = -7 + 6
-2z = -1
z = {{{(-1)/(-2)}}}
z = +.5
;
Find x using the last original equation:
-x + .5 = 0
-x = -.5
x = + .5
:
Solutions: x=.5; y=-2; z=.5
:
Check solution in 1st original equation x - 4y + z = 9
.5 - 4(-2) + .5 = 9
.5 + 8 + .5 = 9