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If the linear system has

3x-5y+6z=4
-3x-8y-5z=-3
-9x-37y+hz=k
has infinitely many solutions, then k= -------and h=--------

1 Answer

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Final answer:

If the linear system has infinitely many solutions, the value of k is undetermined and h is -6/63.

Step-by-step explanation:

If the linear system has infinitely many solutions, then the determinant of the coefficient matrix would be zero. To find the determinant, we set up the matrix and calculate:

| 3 -5 6 |

|-3 -8 -5 | = 0

|-9 -37 h |

By expanding the determinant, we get the equation 378h + 72 = 0. Solving for h, we find h = -6/63. Since k is not given in the equation, we cannot determine its value.

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