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help with solving the system of equations

3x+4y+z=7
2y+z=3
-5x+3y+8z=-31

• math -

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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