Solve the system of equations 4x+y−2z=3x+14y−12z=342x+12y−z=1. If the system is inconsistent or has dependent equations, say so.
Multiplying each side of equation 2 by 4 gives equation 1, so these two equations are dependent. Equation 1 and equation 3 are not equivalent, however, multiplying each side of equation 3 by 12 does not give equation 1. Instead, we obtain two equations with the same coefficients, but with different constant terms. Thus, the system is inconsistent and the solution set is \cancel0.
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