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Sagot :
Step 1: Problem
-x - 3y + 3z = 21
x + 4y + 5z = -1
5x + 7y - 2z = -34
Step 2: Concept
Apply substitute method to solve the three systems of equation.
Step 3: Method
Name the system of equations
-x - 3y + 3z = 21 ------------------------------ 1
x + 4y + 5z = -1 ------------------------------- 2
5x + 7y - 2z = -34 --------------------------3
From equation 1, make r subject of relation and substitute into 2 and 3
x = -3y + 3z - 21
Next, substitute x in equations 2 and 3.
In 2
- 3y + 3z - 21 + 4y + 5z = -1
y + 8z = -1 + 21
y + 8z = 20 ----------------------------------- (4)
In 3
5(-3y + 3z - 21) + 7y - 2z = -34
-15y + 15z - 105 + 7y - 2z = -34
-8y + 13z = - 34 + 105
-8y + 13z = 71 ------------------------------------- (5)
from 4, make y subject and substitute in 5
y = 20 - 8z
In 5
-8(20 - 8z) + 13z = 71
-160 + 64z + 13z = 71
77z = 71 + 160
77z = 231
z = 231/77
z = 3
y = 20 - 8(3)
y = 20 - 24
y = -4
x = -3y + 3z - 21
x = -3(-4) + 3(3) - 21
x = 12 + 9 - 21
x = 0
Step 4: Final answer
x = 0, y = -4 z = 3
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