The solution of the system of linear equations is (x, y, z) = (4, 6, - 1).
How to solve a system of linear equation by substitution
In this question we are asked to find the solution to the system of linear equations by substitution method, which consist in taking advantage of explicit form of linear equations to reduce the number of variables to one and then determine the value of the remaining variables by evaluating the rest of the expressions in explicit form. We find the following expressions:
- x - y - z = - 8 (1)
- 4 · x + 4 · y + 5 · z = 7 (2)
2 · x + 2 · z = 4 (3)
First, clear x in (1):
x = 8 - y - z
Second, substitute x in (2, 3):
- 4 · (8 - y - z) + 4 · y + 5 · z = 7
- 32 + 4 · y + 4 · z + 4 · y + 5 · z = 7
- 32 + 8 · y + 9 · z = 7
8 · y + 9 · z = 39 (2b)
2 · (8 - y - z) + 2 · z = 4
16 - 2 · y - 2 · z + 2 · z = 4
16 - 2 · y = 4
2 · y = 12
y = 6 (3b)
Third, substitute in (2b):
8 · 6 + 9 · z = 39
48 + 9 · z = 39
9 · z = - 9
z = - 1
Fourth, substitute in (1):
x = 9 - 6 - (- 1)
x = 9 - 6 + 1
x = 4
The solution of the system of linear equations is (x, y, z) = (4, 6, - 1).
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