Answer:
x + y - z = 5
2x + 3y + 4z = 0
5x + 6y + 7z = 3
x = 5 - y + z
2x + 3y + 4z = 0
2(5 - y + z) + 3y + 4z = 0
10 - 2y + 2z + 3y + 4z = 0
-2y + 3y + 2z + 4z + 10 = 0
y + 6z = -10
x = 5 - y + z
5x + 6y + 7z = 3
5(5 - y + z) + 6y + 7z = 3
25 - 5y + 5z + 6y + 7z = 3
-5y + 6y + 5z + 7z = 3 - 25
y + 12z = -22
y + 6z = -10
- y + 12z = -22
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-6z = 12
----- -----
-6 -6
z = -12/6 ÷ 6/6
z = -2
y + 6z = -10
y + 6(-2) = -10
y - 12 = -10
y = -10 + 12
y = 2
x = 5 - y + z
x = 5 - 2 + (-2)
x = 5 - 2 - 2
x = 3 - 2
x = 1
check:
x + y - z = 5
1 + 2 - (-2) = 5
1 + 2 + 2 = 5
5 = 5 ✔️
2x + 3y + 4z = 0
2(1) + 3(2) + 4(-2) = 0
2 + 6 - 8 = 0
8 - 8 = 0
0 = 0 ✔️
5x + 6y + 7z = 3
5(1) + 76(2) + 7(-2)= 3
5 + 12 - 14 = 3
17 - 14 = 3
3 = 3 ✔️
x = 1
y = 2
z = -2
