Problem: find the solution in the system of equations.
x-2y-z=-2
x+2y+z=0
y+3z=3
1) x - 2y - z = -2
2) x + 2y + z = 0
3) y + 3z = 3
add eq. 2 to eq. 1
x - 2y - z = -2
+(x + 2y + z = 0)
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2x = -2
x = -1
mult. eq. 2 by 3
3(x + 2y + z = 0)
4) 3x + 6y + 3z = 0
subtract eq. 3 from eq. 4
3x + 6y + 3z = 0
-( y + 3z = 3)
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3x + 5y = -3
5) 3x + 5y = -3
Solve for y.
3x + 5y = -3
3(-1) + 5y = -3
-3 + 5y = -3
5y = 0
y = 0
use eq. 3 to solve for z
y + 3z = 3
0 + 3z = 3
3z = 3
z = 1
Answer: x = -1, y = 0, z = 1