SOLUTION: Solve the system of equations, thank you 3x + 4y + z = 7 2y + z = 3 -5x + 3y + 8z = -31

Question 204756: Solve the system of equations, thank you
3x + 4y + z = 7
2y + z = 3
-5x + 3y + 8z = -31
Answer by alicealc(293) (Show Source): You can put this solution on YOUR website!
eliminate x from the 1st and 3rd equations by:
multiply the 1st equation by 5:
15x + 20y + 5z = 35
multiply the 3rd equation by 3:
-15x + 9y + 24z = -93
add them up:
15x + 20y + 5z = 35
-15x + 9y + 24z = -93
------------------------- (+)
29y + 29z = -58
------------------ (divide each side by 29)
y + z = -2

subtract the 2nd equation from the problem with this new equation:
2y + z = 3
y + z = -2
------------- (-)
y = 5

substitute the value of y into 2nd equation:
2y + z = 3
2*5 + z = 3
10+ z = 3
z = 3 - 10 = -7

substitute the value of y and z into the 1st equation:
3x + 4y + z = 7
3x + 4*5 + (-7) = 7
3x + 20 - 7 = 7
3x + 13 = 7
3x = 7 - 13
3x = -6
x = -6/3 = -2

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

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