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eq.1 4x+4y+3z = 6
eq.2 4x+7y+5z = 5
eq.3 5x+3y+3z = 7
We will begin by eliminating z from eqs.1 and 3
Multiply eq.1 through by -1 and to it add eq.3
-4x-4y-3z = -6
eq.3 5x+3y+3z = 7
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eq.4 x- y = 1
Next we eliminate the same variable z from eqs. 1 and 2
Multiply eq.1 by -5 and eq. 2 by 3 and add them
-20x-20y-15z = -30
12x+21y+15z = 15
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eq.5 -8x+ y = -15
We can eliminate y by adding equations 4 and 5
eq.4 x - y = 1
eq.5 -8x + y = -15
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-7x = -14
x = 2
Substitute x = 2 into eq.4
x - y = 1
2 - y = 1
-y = -1
y = 1
Substitute x = 2 and y = 1 in eq.q
eq.1 4x+4y+3z = 6
4(2)+4(1)+3z = 6
8+4+3z = 6
12+3z = 6
3z = -6
z = -2
Solution: x=2, y=1, z=-2
Edwin
