Solving for h in a Consistent Linear System

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To determine the value of h for the matrix to represent a consistent linear system, the discussion revolves around the augmented matrix formed by the equations 1x - 3y = -2 and 5x + hy = -7. The contributors analyze the implications of different values of h, concluding that h cannot be 15, as this leads to an inconsistent system with a row of zeros and a non-zero constant. The row reduction process reveals that for the system to remain consistent, h must be adjusted to avoid creating contradictions in the equations. Ultimately, the focus is on finding the specific conditions under which the system remains solvable.
beanryu
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hello.
please help!

this is the problem:
determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

1 -3 -2
5 h -7

i tried replacing and scaling... but it seems there are always 2 variable in this.
can you guys help me solve this problem?
 
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Is that an augmented system:

1x-3y=-2
5x+hy=-7

?
 
is that not?
 
is the answer any number... because with everynumber, there is a different solution to x and y?... probably true?
 
ohkay... i think i got the answer... h cannot be 15, because than it will be

1 -3 -2
0 0 3
this show that it will be inconsistent...
 
No, you've "lost a sign". The row reduction of
\left[\begin{array}{ccc}1 & -3 & -2 \\ 5 & h & 7\end{array}\right]
is
\left[\begin{array}{ccc}1 & -3 & 2\\ 0 &h+ 15 & 3\end{array}\right]

What must h be so that is inconsistent?
 

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