SOLUTION: Use Gaussian elimination to solve the system w + z = 380 w + x = 600 x - y = 170 y - z = 50 The solution set is {_,_,_}

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Question 306408: Use Gaussian elimination to solve the system
w + z = 380
w + x = 600
x - y = 170
y - z = 50
The solution set is {_,_,_}
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
w + z = 380
w + x = 600
x - y = 170
y - z = 50

id start working backwards
y-z=50solve for y
highlight%28y=z%2B50%29
x-y=170 solve for x
x=170%2By fill in y with what it equals
x=170%2B%28z%2B50%29
highlight%28x=220%2Bz%29
w%2Bx=600solve for w
w=600-x substitute for x
w=600-%28220%2Bz%29
highlight%28w=380%2Bz%29
w%2Bz=380 solve for z
z=380-w substitute for w
z=380-%28380%2Bz%29
0=0
so z can be any number
so if z=1 then x=221 y=51 w=381
if z=2 then x=222 y=52 w=382
if z=3 then x=223 y=53 w=383
and so on
{z=|(-∞,+∞)}
all real numbers