A linear system of equations is considered consistent if it contains at least one solution. The system is consistent whether it has exactly one or infinitely many solutions. If the system lacks a solution, it is inconsistent.
given,
2x1 – x2 = h
-6x1 + 3x2 = k
To find the system’s consistent values for ℎ and 𝑘, we compare the row-reduced equations.
The second row shouldn’t result in a contradiction for the system to remain consistent. There would be a contradiction if:
The system is consistent for any h and k such that k = −3h.
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