Question

For the following system to be consistent, 4x+5y+5z=−7; 18x−5y+kz=4 and 7x−5y+6z=7 we must have, k is not equal to:

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Answer 1

To determine the value of k that would make the system consistent, we need to use the method of elimination.

Step-by-step explanation:

To determine the value of k that would make the system consistent, we need to use the method of elimination. We have the following system of equations:

4x + 5y + 5z = -7

18x - 5y + kz = 4

7x - 5y + 6z = 7

By adding the first and third equations, we can eliminate y and solve for x and z. This gives us the equation 11x + 11z = 0. Now, we can substitute the values of x = 1 and z = -1 into the second equation to find k. Solving for k, we get k = 10. Therefore, k is not equal to 10 for the system to be consistent.