Question 226538
2x + y - 3z = 5
x + y - 3z = 1
x - z = 4
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2x + y - 3z = 5
x + y - 3z = 1
-------------- Subtract
x = 4
-----------
x - z = 4
z = 0
----------
x + y - 3z = 1
4 + y = 1
y = -3
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linear equation by method of elimination 
9x - 2y = 7 times -2 --> -18x + 4y = -14
-18x + 4y = -7
These are inconsistent, no solution.  It can't equal both -7 and -14
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linear equation by method of elimination 
-3x - y = -3 times 2 --> -6x - 2y = -6
x + 2y = -4 
-6x - 2y = -6
-----------------  Add
-5x = -10
x = 2
---------
2 + 2y = -4
y = -3
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linear equation by any convenient method 
x - 2y = -13
-2x - 2y = -4 
----------------- Subtract
3x = -9
x = -3
--------
y = 5