Est form. Lessons 3-5) 2 9
1 answer:
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Answer:
If k = −1 then the system has no solutions.
If k = 2 then the system has infinitely many solutions.
The system cannot have unique solution.
Step-by-step explanation:
We have the following system of equations
The augmented matrix is
The reduction of this matrix to row-echelon form is outlined below.
The last row determines, if there are solutions or not. To be consistent, we must have k such that
Case k = −1:
If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.
Case k = 2:
This gives the infinite many solution.
Step-by-step explanation:
First, let's move the to the right-hand side so we can determine what constant we'll need on the left-hand side to complete the square:
From here, since the coefficient of the term is
, we know the square will be
(since
it's half of
).
To complete this square, we will need to add to both sides of the equation:
Now we can take the square root of both sides to figure out the solutions to :