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Sagot :
Total Equations are 3:
5x-3y+4z=-16→(1)
-4x+2y-3z=12→(2)
-x+5y+7z=32→(3)
Step 1: Select the equations (1) and (3), and eliminate the variable x.
(5x - 3y + 4z = -16) x 1 → 5x - 3y + 4z = -16
( -x + 5y + 7z = 32) x 5 → + -5x + 25y+ 35z = 160
22y+ 39z = 144 → (4)
Step 2: Select the equations (2) and (3), and eliminate the variable x.
( -4x + 2y - 3z = 12) x 1 → -4x + 2y - 3z = 12
( -x + 5y + 7z = 32) x 4 → - -4x + 20y + 28z = 128
- 18y - 31z = -116→ (5)
Step 3: Select the equations (4) and (5), and eliminate the variable y.
(22y + 39z = 144) x 9 →198y + 351z = 1296
(-18y - 31z = -116) x 11 → + -198y - 341z = -1276
10z = 20
10z/10 = 20/10
z = 2
Therefore, z = 2.
For y, plug-in z = 2 in equation 5.
-18y - 31z = -116
-18y - 31(2) = -116
-18y + 64 = -116
-18y = -116 + 62
-18y = -54
-18y/-18 = -54/-18
y = 3
Therefore, y = 3.
For x, plug-in y = 3 and z = 2 in Equation 3.
-x + 5y + 7z = 32
-x + 5(3) + 7(2) = 32
-x + 15 + 14 = 32
-x + 29 = 32
-x = 32 - 29
-x = 3
-x/-1 = 3/-1
x = -3
Therefore, x = -3.
In Summary:
x = -3
y = 3
z = 2
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