Posted by **Paula** on Monday, March 22, 2010 at 3:56am.

help with solving the system of equations

3x+4y+z=7

2y+z=3

-5x+3y+8z=-31

- math -
**Reiny**, Monday, March 22, 2010 at 8:37am
the middle equation is nice and gives us

z = 3-2y

sub that into the first and third

1) 3x + 4y + 3 - 2y = 7

3x + 2y = 4 (#1)

3) -5x + 3y + 8(3-2y) = -31

-5x + 3y + 24 - 16y = -31

-5x - 13y = -55

5x + 13y = 55 (#3)

#1 by 5: 15x + 10y = 20

#3 by 3: 15x + 39y = 165

subtract them ...

29y = 145

y = 5

back in #1

3x + 2y = 4

3x + 10 = 4

x = -2

back into the middle

2y + z = 3

10 + z = 3

z = -7

x = -2, y = 5, z = -7

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