2.
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x | + | 3y | - | z | = | 6 | multiply through by 2 to get | 2x | + | 6y | - | 2z | = | 12 |
4x | - | 2y | + | 2z | = | -10 | multiply through by 3 to get | 12x | - | 6y | + | 6z | = | -30 |
6x | + | z | = | -12 | multiply through by -4 to get | -24x | - | 4z | = | 48 |
Add these three equations together to get
-10x = 30 Divide both sides by -10 .
x = -3
Use this value for x in the third given equation to find z .
6(-3) + z = -12 Subtract 6(-3) from both sides.
z = -12 - 6(-3) = -12 + 18 = 6
Now we can find y using the first given equation.
-3 + 3y - 6 = 6
3y = 15
y = 5
So x = -3 , y = 5 , and z = 6