I will assume you are using elimination, although there are several other methods.
In elimination, you first have to decide which variable you want to eliminate. Usually that is determined by choosing the simplest coefficients, in this case I would go for z
1st: x-y + 3z = 4
2nd times 3: 3x + 6y - 3z = -9
add them 4x + 5y = -5 (#4)
2nd times 2: 2x + 4y - 2z = -6
3rd: 4x + 3y + 2z = -5
add them 6x + 7y = -11 (#5)
#4 times 3 : 12x + 15y = -15
#5 times 2: 12x + 14y = -22
y = 7
back into #4 : 4x + 35 = -5
4x = -40
x = -10
back into #1 : -10 - 7 + 3z = 4
3z = 21
z = 7
x = -10 , y = 7, z = 7
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