Solve the following simultaneous equations: 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31  

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We have the following simultaneous equations to solve:

3x + 4y + z = 7 …(1)

2y + z = 3 …(2)

-5x + 3y + 8z = -31 …(3)

From (2), we get 2y + z = 3

=> z = 3 – 2y

substitute in (1)

=> 3x...

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We have the following simultaneous equations to solve:

3x + 4y + z = 7 …(1)

2y + z = 3 …(2)

-5x + 3y + 8z = -31 …(3)

From (2), we get 2y + z = 3

=> z = 3 – 2y

substitute in (1)

=> 3x + 4y + 3 – 2y = 7

=> 3x + 2y = 4

=> x = (4 – 2y)/3

substitute z and x in terms of y in (3)

=> -5(4 – 2y)/3 + 3y + 24 – 16y = -31

=> -20/3 + 10y/3 + 3y + 24 – 16y = -31

=> -20 + 10y + 9y + 72 – 48y = -93

=> -29y = -145

=> y = 5

z = 3 – 2y = 3 – 10 = -7

x = (4 – 2y)/3 = (4 – 10)/3 = -2

The value of x = -2, y = 5 and z = -7

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