Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z = 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2

The system has solution when:

The system has no solution when:

Step-by-step explanation:

First rewrite the system in its augmented matrix form

Let´s apply row reduction process to  its associated augmented matrix:

Now we have this:

We can conclude now:

The system has no solution when:

And the system has solution when:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

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