SOLUTION: 2x+y=8 y+3z=5 z+2w=1 5w+3x=9 solve the equations for x,y,w,z

Question 21423: 2x+y=8
y+3z=5
z+2w=1
5w+3x=9
solve the equations for x,y,w,z
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
2x + y = 8
y + 3z = 5
(a) solve each equation for y
y = 8 - 2x
y = 5 - 3z
(b) solve the third equation for z
z + 2w = 1
z = 1 - 2w
from (a)
8 - 2x = 5 - 3z
substitute (1-2w) for z, the result from (b)
8 - 2x = 5 - 3(1-2w)
8 - 2x = 5 - 3(1-2w)
8 - 2x = 5 - 3 + 6w
(c) 8 - 2x = 2 + 6w
solve the fourth equation for x
5w + 3x = 9
3x = 9 - 5w
x = 3 - (5/3)w
substitute this result into (c)
8 -2(3 - (5/3)w) = 2 + 6w
8 - 6 + (10/3)w = 2 + 6w
8 - 6 - 2 = (8/3)w
0 = (8/3)w
w = 0
from the fourth equation,
5(0) +3x = 9
x = 3
from the 1st equation,
2(3) + y = 8
y = 2
from the 2nd equation,
(2) + 3z = 5
z = 1
so,
x = 3
y = 2
z = 1
w = 0
plug these values back into all four equations to verify them

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