Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.)
3x − 2y + 4z = 23
2x + y − 2z = −1
x + 4y − 8z = −25
Let's denote the three equations as:
Eqn (1): 3x - 2y + 4z = 23
Eqn (2): 2x + y - 2z = -1
End (3): x + 4y - 8z = -25
Eqn(1) + 2 x Eqn (2) gives us: 7x = 23 - 2 = 21; Hence x = 21 / 7 = 3
Let's substitute x = 3 in all three equation and see:
From eqn (1) we get: 3 x 3 - 2y + 4z = 23 or, -2y + 4z = 14 or, y - 2z = -7
From eqn (2) w...
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