SOLUTION: x-y+5z=22 2x + z= 5 x+4y+z=17

Question 162411This question is from textbook
: x-y+5z=22
2x + z= 5
x+4y+z=17 This question is from textbook

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
not sure if this is supposed to be a matrix algebra problem or just a simultaneous equation problem that needs to be solved without using matrix algebra.
i solved it without using matrix algebra.
it became a lot easier because one of the equations was missing the y value.
the equations are:
x - y + 5z = 22
2x + z = 5
x + 4y + z = 17
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multiply the first equation by 4 and multiply the second equation by (-2.5).
the equations become
4x - 4y + 20.0z = 88
-5x - 2.5z = -12.5
x + 4y + z = 17
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adding all 3 equations together and the sum becomes
0x + 0y + 18.5z = 92.5
z = 5
---------
substituting 5 for z in the second equation and it becomes
2x + 5 = 5
2x = 0
x = 0
---------
substituting 5 for z and 0 for x in the third equation and it becomes
0 + 4y + 5 = 17
4y = 12
y = 3
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values are:
x = 0
y = 3
z = 5
----------
substituting in all equations yields the identity equation in each so all values are good in all equations.
-----
identity equation would be something like
22 = 22
5 = 5
17 = 17
which is what i got when i substituted in each equation.
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