Question

Solve the following system of equations

3x - 4y + z = -5
x-y-z = -10
6x - 8y + 2z = 10

Answer 1

Notice that the left side of the third equation is 2 times the left side of the first equation:

6x - 8y + 2z = 2 (3x - 4y + z)

The first equation says

3x - 4y + z = -5

while the third equation would reduce to

2 (3x - 4y + z) = 10 ⇒ 3x - 4y + z = 5

but -5 ≠ 5, so there is no solution to the system.